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+# 📐 Design Notes: Complex Number Arithmetic Module
+**Team:** Group 13
+**Target Branch:** `Group_B`
+
+---
+
+## 1. Architectural Approach
+* **Modularity:** The feature is logically encapsulated within an independent `ComplexCalculator` class. This ensures clean integration with the base system without accidentally altering the core `Calculator` class .
+* **Separation of Concerns:** The module strictly divides responsibilities into three internal domains: string parsing, mathematical execution, and error management.
+
+## 2. Input Parsing Strategy
+* **Constraint:** The system strictly requires mathematical inputs to be provided as continuous strings (e.g., `'(3+2j)*(5+3j)'`).
+* **Solution:** We implemented Python's `re` (Regular Expressions) module to act as the extraction engine. 
+    * *Pre-processing:* All arbitrary whitespaces are stripped to standardize the user's input.
+    * *Extraction:* The regex pattern `r'\(([^)]+)\)([\+\-\*\/])\(([^)]+)\)'` dynamically isolates the first operand, the arithmetic operator, and the second operand into exact capture groups.
+
+## 3. Mathematical Implementation
+* **Object Casting:** Extracted string operands are safely cast directly to Python's native `complex()` objects, inherently supporting the required $a+bj$ mathematical representation.
+***Core Arithmetic:** Standard Python overloaded operators (`+`, `-`, `*`, `/`) handle the required addition, subtraction, multiplication, and division operations.
+* **Advanced Computations:** Standard mathematical libraries are utilized for complex plane metrics.
+    * **Magnitude:** Calculated using the built-in `abs(z)` function to efficiently compute $\sqrt{a^2 + b^2}$.
+    * **Phase:** Computed using `cmath.phase(z)` to guarantee accurate quadrant mapping and return the angle in radians.
+* **Output Formatting:** Raw mathematical results are dynamically reformatted back into the strictly required `a+bj` string notation before being returned to the main process.
+
+## 4. Error Handling & Validation
+* **Syntax Validation:** The regex parser acts as the first line of defense. Unmatched patterns or invalid characters raise an immediate `ValueError`.
+* **Boundary Conditions:** A programmatic check intercepts mathematical impossibilities, such as dividing by `(0+0j)`, raising a descriptive exception to prevent catastrophic system crashes.
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diff --git a/FinalReport.md b/FinalReport.md
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+# Software Engineering Laboratory: Final Project Report
+**Project:** Extensible Calculator System - Complex Number Arithmetic
+**Team:** Group 13
+**Target Integration Branch:** `Group_B`
+
+---
+
+## 1. Introduction and Objective
+The primary objective of this laboratory experiment was to gain practical experience with industry-style software development practices. This was achieved by applying all phases of the Software Development Life Cycle (SDLC) to a single, extensible Python-based calculator system. 
+
+Our specific team, Group 13, was tasked with analyzing, designing, implementing, and testing the **Complex Number Arithmetic** extension. The goal was to build a modular feature that integrates seamlessly with the base calculator application while adhering to strict version control and testing protocols.
+
+## 2. Requirement Analysis
+During the initial phase of the SDLC, we identified the specific functional and non-functional requirements for the complex number module. 
+
+**Functional Requirements:**
+* The module must accept user input exclusively as a continuous string (e.g., `'(3+2j)*(5+3j)'`).
+* It must support the standard $a+bj$ mathematical representation.
+* The system must perform standard arithmetic operations: addition, subtraction, multiplication, and division of complex numbers.
+* The system must compute advanced metrics: magnitude and phase.
+
+**Non-Functional Requirements & Constraints:**
+* Code must be highly modular and maintainable, isolating complex logic from the core `Calculator` class.
+* All errors (like malformed strings or division by zero) must be handled gracefully without crashing the main application.
+
+## 3. System Architecture and Design
+To fulfill the requirements, we designed an independent software component to handle all complex domain logic. 
+
+* **Object-Oriented Encapsulation:** We designed a standalone `ComplexCalculator` class. This ensures that the base system remains untouched and adheres to the Open/Closed Principle (open for extension, closed for modification).
+* **String Parsing Engine:** Because inputs are strict strings, we designed a parsing layer using Python's Regular Expressions (`re` module). We engineered the pattern `r'\(([^)]+)\)([\+\-\*\/])\(([^)]+)\)'` to dynamically isolate the first operand, the arithmetic operator, and the second operand, bypassing arbitrary whitespace issues.
+* **Mathematical Delegation:** Rather than manually calculating complex arithmetic, the design leverages Python's native `complex()` casting capabilities and the standard `cmath` library to guarantee mathematical precision.
+
+## 4. Implementation Details
+The implementation phase translated our design into functional Python code within the `complex.py` module. 
+
+* **Arithmetic Execution:** Once the regex engine extracts the string components, they are cast to `complex` objects. Python's overloaded operators process the calculation, and a custom `_format_result` method reconstructs the output back into the required $a+bj$ string format.
+* **Magnitude Computation:** Implemented using the built-in `abs(z)` function, which efficiently processes the underlying $\sqrt{a^2 + b^2}$ calculation.
+* **Phase Computation:** Implemented using `cmath.phase(z)`, which safely maps the angle in radians across all four quadrants.
+* **Exception Handling:** A robust `try-except` block is implemented to catch `ValueError` instances. If the regex fails to find a match, or if a zero-division occurs during evaluation, the module halts the calculation and returns a descriptive error string.
+
+## 5. Software Testing and Quality Assurance
+Test-driven development practices were strictly followed. A comprehensive unit test suite was developed in `test_complex.py` using Python's native `unittest` framework to ensure high code quality and test coverage.
+
+The test suite validates the system against three core paradigms:
+* **Normal Cases:** Tests verify standard execution for all operations (e.g., asserting that `(1+2j)+(2+3j)` successfully evaluates to `3.0+5.0j`).
+* **Boundary Conditions:** Edge cases were tested, most notably asserting that evaluating `(5+5j)/(0+0j)` correctly raises a `ValueError` rather than triggering a system-level math fault.
+* **Invalid Input Handling:** The parser's resilience was tested by injecting malformed strings (e.g., missing parentheses, alphabetic characters, and unsupported operators). The tests confirm that the system correctly identifies and rejects these inputs.
+
+## 6. Version Control and Configuration Management
+To support concurrent development across 20 groups without code conflicts, strict Git configuration management protocols were followed.
+
+* **Repository Forking & Cloning:** The main project repository was forked to an isolated environment. As Group 13 falls into the second cohort, we specifically cloned and targeted the `Group_B` branch for our baseline code.
+* **Feature Branching:** Development was conducted entirely within an isolated feature branch (`FeatureB_13`) to prevent contamination of the group's integration branch.
+* **Integration and Merging:** Following successful local testing, code updates were committed incrementally. The final feature was pushed to the remote fork, and a Pull Request was generated targeting the main repository's `Group_B` branch, ensuring zero merge conflicts with other teams.
+
+## 7. Conclusion
+Through this experiment, Group 13 successfully applied the complete Software Development Life Cycle. By conducting thorough requirement analysis, designing a modular regex-driven architecture, implementing robust unit tests, and adhering to strict Git branching strategies, we successfully delivered a highly functional and reliable Complex Number Arithmetic module for the extensible calculator system.
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diff --git a/complex.py b/complex.py
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+import cmath
+import re
+
+class ComplexCalculator:
+    def evaluate(self, expression: str) -> str:
+        """
+        Parses and evaluates a complex number expression.
+        Example input: '(3+2j)*(5+3j)'
+        """
+        # Remove all spaces so we don't have to worry about weird spacing
+        expr = expression.replace(" ", "")
+
+        # Regex to match the arithmetic format: (a+bj) operator (c+dj)
+        # Group 1: First number, Group 2: Operator, Group 3: Second number
+        pattern = r'\(([^)]+)\)([\+\-\*\/])\(([^)]+)\)'
+        match = re.match(pattern, expr)
+
+        if match:
+            c1_str = match.group(1)
+            operator = match.group(2)
+            c2_str = match.group(3)
+            return self._perform_arithmetic(c1_str, operator, c2_str)
+
+        # Regex to handle Magnitude: e.g., 'mag(3+2j)'
+        mag_match = re.match(r'mag\(([^)]+)\)', expr)
+        if mag_match:
+            return self.magnitude(mag_match.group(1))
+
+        # Regex to handle Phase: e.g., 'phase(3+2j)'
+        phase_match = re.match(r'phase\(([^)]+)\)', expr)
+        if phase_match:
+            return self.phase(phase_match.group(1))
+
+        raise ValueError("Invalid complex number expression format.")
+
+    def _perform_arithmetic(self, c1: str, operator: str, c2: str) -> str:
+        # Convert strings to actual complex numbers
+        try:
+            z1 = complex(c1)
+            z2 = complex(c2)
+        except ValueError:
+            raise ValueError("Invalid format. Use a+bj notation.")
+
+        # Perform the actual math
+        if operator == '+':
+            result = z1 + z2
+        elif operator == '-':
+            result = z1 - z2
+        elif operator == '*':
+            result = z1 * z2
+        elif operator == '/':
+            if z2 == 0:
+                raise ValueError("Division by zero")
+            result = z1 / z2
+        else:
+            raise ValueError("Unknown operator")
+
+        return self._format_result(result)
+
+    def magnitude(self, c_str: str) -> str:
+        z = complex(c_str)
+        # Magnitude is calculated as sqrt(a^2 + b^2)
+        return str(abs(z))
+
+    def phase(self, c_str: str) -> str:
+        z = complex(c_str)
+        # Phase is calculated in radians
+        return str(cmath.phase(z))
+
+    def _format_result(self, z: complex) -> str:
+        """Formats the output back to a readable a+bj string."""
+        # Ensure the imaginary part always has a + or - sign
+        sign = '+' if z.imag >= 0 else '-'
+        return f"{z.real}{sign}{abs(z.imag)}j"
+
+# # Example Usage (You can delete this part in your final file, it's just to show you how it works):
+# if __name__ == "__main__":
+#     calc = ComplexCalculator()
+#     print(calc.evaluate("(3+2j)*(5+3j)"))  # Output: 9.0+19.0j
+#     print(calc.evaluate("(1+2j)+(2+3j)"))  # Output: 3.0+5.0j
+#     print(calc.evaluate("mag(3+4j)"))      # Output: 5.0
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diff --git a/test_complex.py b/test_complex.py
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+import unittest
+import math
+from complex import ComplexCalculator
+
+class TestComplexCalculator(unittest.TestCase):
+
+    def setUp(self):
+        # This creates a new calculator object before each test runs
+        self.calc = ComplexCalculator()
+
+    # --- NORMAL CASES ---
+    def test_addition(self):
+        # (1+2j) + (2+3j) = 3+5j
+        result = self.calc.evaluate("(1+2j)+(2+3j)")
+        self.assertEqual(result, "3.0+5.0j")
+
+    def test_subtraction(self):
+        # (5+5j) - (2+1j) = 3+4j
+        result = self.calc.evaluate("(5+5j)-(2+1j)")
+        self.assertEqual(result, "3.0+4.0j")
+
+    def test_multiplication(self):
+        # (1+2j) * (3+4j) = -5+10j
+        result = self.calc.evaluate("(1+2j)*(3+4j)")
+        self.assertEqual(result, "-5.0+10.0j")
+
+    def test_division(self):
+        # (10+5j) / (2+0j) = 5+2.5j
+        result = self.calc.evaluate("(10+5j)/(2+0j)")
+        self.assertEqual(result, "5.0+2.5j")
+
+    def test_magnitude(self):
+        # Magnitude of 3+4j is exactly 5.0 (Pythagorean triple: 3^2 + 4^2 = 5^2)
+        result = self.calc.evaluate("mag(3+4j)")
+        self.assertEqual(result, "5.0")
+
+    def test_phase(self):
+        # Phase of 0+1j is exactly pi/2 (90 degrees)
+        result = self.calc.evaluate("phase(0+1j)")
+        # Since float comparison can be tricky, we round it for testing
+        self.assertEqual(round(float(result), 4), round(math.pi / 2, 4))
+
+    # --- BOUNDARY CONDITIONS & INVALID INPUTS ---
+    def test_divide_by_zero(self):
+        # The system must catch dividing by zero and raise a ValueError
+        with self.assertRaises(ValueError) as context:
+            self.calc.evaluate("(5+5j)/(0+0j)")
+        self.assertTrue("Division by zero" in str(context.exception))
+
+    def test_invalid_string_format(self):
+        # Testing what happens if the user types complete garbage
+        with self.assertRaises(ValueError):
+            self.calc.evaluate("hello_world")
+
+    def test_missing_parentheses(self):
+        # The regex strictly expects parentheses. Missing them should fail.
+        with self.assertRaises(ValueError):
+            self.calc.evaluate("3+2j*5+3j")
+
+    def test_invalid_operator(self):
+        # Testing an operator that isn't supported by the regex
+        with self.assertRaises(ValueError):
+            self.calc.evaluate("(3+2j)^(5+3j)")
+
+if __name__ == "__main__":
+    unittest.main()
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