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write the trigonometric forms of the complex numbers

+1 vote

(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).

asked Jan 27, 2015 in TRIGONOMETRY by anonymous

3 Answers

+1 vote

(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:

.

answered Jan 28, 2015 by yamin_math Mentor
+1 vote

(b)

Step 1:

The trigonometric form of complex number is .

Now perform the indicated operation using the trigonometric form.

image

Use the Quotient rule of two complex numbers :

Let  image and image.

image

image

Solution:

image.

answered Jan 28, 2015 by yamin_math Mentor
+1 vote

(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.

image

Solution:

image.

answered Jan 28, 2015 by yamin_math Mentor

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