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Determine the polar form of the complex number 3-2i complex plane and polar formOf complex numbers?

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Determine the polar form of the complex number 3-2i complex plane and polar formOf complex numbers?

Determine the polar form of the complex number 3-2i Express the angle theta in degrees, where 0<theta<360 and round numeric entries in the answer to two decimal places
asked Feb 14, 2015 in PRECALCULUS by anonymous

1 Answer

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Step 1:

The complex number is image.

Consider image.

Polar form of a complex number image is image   (1)

Here image and image.

Where image is magnitude of complex number and is defined as image and image is argument of image.

Step 2:

Magnitude of complex number  image is image.

Here image and image.

image and image.

image and image

cosine function is positive and sine function is negative, which means that image lies in fourth quadrant.

Thus , angle satisfies both functions is image.

Substitute image and image in  expression (1).

image

Solution:

The polar form of the complex number image is image.

answered Feb 16, 2015 by cameron Mentor
edited Feb 16, 2015 by cameron

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