Some operations with complex numbers are most easily performed when the numbers are in trigonometric form.

Here's how division multiplication operations work.

## Multiplication

Consider two complex numbers in trigonometric form. . The product It is given by:

Remembering the arcing formulas:

Like this:

Note that the product is a complex number whose modulus is the product of the factor modules and whose argument is the sum of the factor arguments.

**Example**

Calculate the product , with :

*Resolution *

- The module of it's product .
- The argument of is given by the sum .

Like this:

## Division

Consider two complex numbers in trigonometric form:

.

The quotient It is given by:

Remembering the arc difference formulas:

And of the fundamental trigonometric relationship:

Like this:

Note that the quotient is a complex number whose modulus is the quotient of the dividend and divisor modules, and whose argument is the difference of the dividend and divisor arguments.

**Example**

Calculate the quotient , with :

*Resolution *

- The module of is the quotient .
- The argument of is given by the difference

How We do:

Like this: