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Question

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Write mc003-1.jpg in trigonometric form and find their product. 

mc003-2.jpg

asked Dec 4, 2015 in TRIGONOMETRY by anonymous

2 Answers

0 votes

Step 1:

The complex numbers are image and image.

The polar form of a complex number  is .

Where image, imageand .

Here  is the magnitude of the complex number and  is argument of .

Compare the complex number image with .

Here image and image.

Magnitude of image:

image

image.

Substitute image, image and image in image and image.

image and image

image and image.

Since the cosine function is negative and sine function is positive, lies in second quadrant.

The angle satisfies both the conditions is image.

Substitute image and image in trigonometric form.

image.

The trigonometric form of image is image.

Step 2:

Compare the complex number image with .

Here image and image.

Magnitude of image:

image

image.

Substitute image, image and image in image and image.

image and image

image and image.

Since both the trigonometric functions are negative, lies in third quadrant.

The angle satisfies both the conditions is image.

Substitute image and image in trigonometric form.

image.

The trigonometric form of image is image.

Solution:

The trigonometric form of image is image.

The trigonometric form of image is image.

answered Dec 4, 2015 by Sammi Mentor
edited Dec 4, 2015 by Sammi
0 votes

The trigonometric form of image is image.

The trigonometric form of image is image.

Product of complex numbers in trigonometric form : .

image

image

image

image.

answered Dec 4, 2015 by Sammi Mentor

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