Divide Complex Numbers Calculator

To divide two complex numbers in rectangular form (a+ib form), use the formula:

Of course, the division is possible only if , which is equivalent to .

Derivation

As you can see, this formula is quite complicated. Fortunately, you don't need to learn it by heart. It is much easier to derive it! There's only one trick you need to remember: start by multiplying both the numerator and denominator by the conjugate of the latter:

Division of complex numbers in much easier in the polar form (r×exp(iφ) form):

We can see that:

• ; and
• .

To most efficiently use our divide complex numbers calculator, follow these steps:

1. Enter the numbers and in the respective boxes. The calculator performs the division .
2. For each number, you can choose if you want to input it in the rectangular form or in the polar form:
   • For the rectangular form, enter the real and imaginary part.
   • For the polar form, enter the magnitude and phase.
3. For the second complex number, you can use the same form as for the first number or the other form - our divide complex numbers calculator will know what to do!
4. The calculator performs the division and returns the quotient in both the rectangular and polar form.

features a whole collection of tools concerning complex numbers, each one emphasizing a slightly different aspect of them:

• Complex number calculator;
• a+bi form calculator;
• Imaginary number calculator;
• Multiply complex numbers calculator;
• Complex number to polar form calculator;
• Complex number to trigonometric form calculator;
• Complex number to rectangular form calculator;
• i calculator; and
• Polar form calculator.