Complex Number Calculator

Complex numbers consist of a real part (a) and an imaginary part (bi), where i is the square root of -1. They are essential in electrical engineering, signal processing, quantum physics, and advanced mathematics.

1. 1

   Enter First Number

   Input the real and imaginary parts of the first complex number (a + bi)

2. 2

   Enter Second Number

   Input the second complex number if needed for binary operations

3. 3

   Select Operation

   Choose add, subtract, multiply, divide, magnitude, phase, or conjugate

4. 4

   View Result

   The result displays as a complex number with magnitude and phase

• 1

  Use polar form (r at angle theta) for easier multiplication and division

• 2

  Magnitude |z| = sqrt(a^2 + b^2) gives the distance from origin

• 3

  The conjugate z* = a - bi is used to simplify division

• 4

  Phase angle theta = arctan(b/a) indicates direction in the complex plane

• Forgetting that i^2 = -1 - when multiplying, (bi)(di) = -bd

• Dividing directly by a complex number - multiply by the conjugate instead

• Confusing Cartesian (a + bi) and polar (r at angle theta) forms

• Ignoring the quadrant when calculating phase angle from arctan