Complex Number Calculator
Perform addition, subtraction, multiplication, and division on complex numbers in rectangular form (a + bi). Shows the result in both Cartesian and polar form (r∠θ°), including magnitude and angle. Used in electrical engineering, signal processing, and advanced mathematics.
Enter the real and imaginary parts for two complex numbers. Select the operation (Add, Subtract, Multiply, Divide) and press Calculate. The result appears in standard form (a + bi), with the magnitude |z|, angle θ in radians, and the equivalent polar notation r∠θ°.
1) Addition: (a+bi)+(c+di) = (a+c)+(b+d)i. 2) Subtraction: (a+bi)−(c+di) = (a−c)+(b−d)i. 3) Multiplication: (a+bi)(c+di) = (ac−bd)+(ad+bc)i (using FOIL and i²=−1). 4) Division: multiply by the conjugate — [(a+bi)(c−di)] / (c²+d²), which eliminates i from the denominator.
Verified Precise