Complex Number Calculator
Perform arithmetic operations on complex numbers including addition, subtraction, multiplication, and division.
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Results
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How It Works
Complex Number Operations
Addition: (a + bi) + (c + di) = (a + c) + (b + d)i
Subtraction: (a + bi) - (c + di) = (a - c) + (b - d)i
Multiplication: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
Division: (a + bi) ÷ (c + di) = [(ac + bd) + (bc - ad)i] ÷ (c² + d²)
Properties
Magnitude: |a + bi| = √(a² + b²)
Conjugate: The conjugate of (a + bi) is (a - bi)
Real Part: The coefficient of the non-imaginary term
Imaginary Part: The coefficient of the imaginary term (i)