SOLUTION: Express the complex number in trigonometric form. 2 - 2i Please help!

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Question 981148: Express the complex number in trigonometric form.
2 - 2i
Please help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2-2i is in the form a%2Bbi where a+=+2 and b+=+-2

Trig form is r%2A%28cos%28theta%29+%2B+i%2Asin%28theta%29%29. We will use the following formulas:

r+=+sqrt%28a%5E2+%2B+b%5E2%29
theta+=+arctan%28b%2Fa%29
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Compute the value of r
r+=+sqrt%28a%5E2+%2B+b%5E2%29
r+=+sqrt%282%5E2+%2B+%28-2%29%5E2%29
r+=+sqrt%284%2B4%29
r+=+sqrt%288%29
r+=+sqrt%284%2A2%29
r+=+sqrt%284%29%2Asqrt%282%29
r+=+2%2Asqrt%282%29
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Now find theta (use a calculator or unit circle).
theta+=+arctan%28b%2Fa%29
theta+=+arctan%28-2%2F2%29
theta+=+arctan%28-1%29
theta+=+-pi%2F4
theta+=+-pi%2F4%2B2pi Adding on 2pi to get the angle between 0 and 2pi
theta+=+7pi%2F4
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So the trig form is

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Final Answer: 2%2Asqrt%282%29%2A%28cos%287pi%2F4%29+%2B+i%2Asin%287pi%2F4%29%29

Note: this is the radian form