Enter the real and imaginary parts of the first and second complex numbers into the calculator to determine the result of the division.

Complex Number Division Formula

The following formula is used to calculate the division of two complex numbers.

Z = (a + bi) / (c + di)Z = ((a*c + b*d) / (c^2 + d^2)) + ((b*c – a*d) / (c^2 + d^2))i

Variables:

  • Z is the result of the division
  • a and b are the real and imaginary parts of the first complex number respectively
  • c and d are the real and imaginary parts of the second complex number respectively

To calculate the division of two complex numbers, multiply the real parts (a and c) and the imaginary parts (b and d) and add the results. Then, square the real and imaginary parts of the second complex number and add the results. Divide the first result by the second result to get the real part of the result. For the imaginary part, multiply the imaginary part of the first complex number and the real part of the second complex number, subtract the product of the real part of the first complex number and the imaginary part of the second complex number, and divide the result by the sum of the squares of the real and imaginary parts of the second complex number.

What is a Complex Number Division?

Complex number division is a mathematical operation involving two complex numbers. It involves the division of the real and imaginary parts of the complex numbers separately, followed by simplification. The process often includes multiplying the numerator and denominator by the conjugate of the denominator to eliminate the imaginary part from the denominator. The result is another complex number.

How to Calculate Complex Number Division?

The following steps outline how to calculate the Complex Number Division using the given formula:

  1. First, determine the real part of the first complex number (a).
  2. Next, determine the imaginary part of the first complex number (b).
  3. Next, determine the real part of the second complex number (c).
  4. Next, determine the imaginary part of the second complex number (d).
  5. Next, calculate the numerator of the formula: a*c + b*d.
  6. Next, calculate the denominator of the formula: c^2 + d^2.
  7. Next, calculate the real part of the result: (a*c + b*d) / (c^2 + d^2).
  8. Next, calculate the imaginary part of the result: (b*c – a*d) / (c^2 + d^2).
  9. Finally, combine the real and imaginary parts to get the final result Z = ((a*c + b*d) / (c^2 + d^2)) + ((b*c – a*d) / (c^2 + d^2))i.

Example Problem:

Use the following variables as an example problem to test your knowledge:

a = 3

b = 2

c = 5

d = 4