write the trigonometric forms of the complex numbers

Question

(a) write the trigonometric forms of the complex numbers, (b) perform the indicated operation using the trigonometric forms, and (c) perform the indicated operation using the standard forms, and check your result with that of part (b).

Answer 1

(a)

Step 1:

The complex number is .

Write the complex number in trigonometric form.

The absolute value of is

and the angle is

So, the trigonometric form of  is

Step 2:

The absolute value of is

and the angle is

So, the trigonometric form of is

The trigonometric form of complex number is

.

Solution:

.

Answer 2

(b)

Step 1:

The trigonometric form of complex number is .

Now perform the indicated operation using the trigonometric form.

Use the Quotient rule of two complex numbers :

Let  and .

Solution:

.

Answer 3

(c)

Step 1:

The complex number is .

Convert the complex number into standard form.

Multiply and divide with the conjugate of .

Step 2:

Now perform the indicated operation.

Solution:

.