Question 176349: How do you simplify (3+i)^57 ?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How do you simplify (3+i)^57
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Convert 3+i to trig form.
You have x = 3 and y = 1
Then r = sqrt(3^2+1) = sqrt(10)
And theta = arctan(1/3) = 18.43 degrees
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Form: (a+bi)^57 = r^57(cos(57(theta)) + i sin(57(theta))
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(3+i)^57 = [sqrt(10)]^57[cos(57(18.43) + i sin(57(18.43))
= 3.1634x10^28(0.874416 - 049227i)
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Cheers,
Stan H.
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