SOLUTION: express the complex number -2 sqrt2 + 2 sqrt2i in the trigonometric form r(cos theta +i sin theta) or rcis(theta)

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Question 85106: express the complex number -2 sqrt2 + 2 sqrt2i in the trigonometric form r(cos theta +i sin theta) or rcis(theta)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
express the complex number -2 sqrt2 + 2 sqrt2i in the trigonometric form r(cos theta +i sin theta) or rcis(theta)
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If complex number is a+bi, then trig form is
rcis(theta) where r=sqrt(a^2+b^2) and theta=arc tan(b/a) is the appropriate
quadrant.
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Your problem:
r= sqrt[-2sqrt2)^2 + (2sqrt2)^2] = sqrt[8+8] = 4
theta = arctan[(2sqrt2)/-2sqrt2]=arctan(-1)= 135 degrees or 315 degrees
But b is positive and a is negative so theta is in the 2nd quadrant.
Therefore theta = 135 degrees or (3/4)pi.
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trig form is 4cis135 or 4cis((3/4)pi)
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Cheers,
Stan H.