# SOLUTION: How do you simplify (3+i)^57 ?

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 Click here to see ALL problems on Complex Numbers Question 176349: How do you simplify (3+i)^57 ?Answer by stanbon(57424)   (Show Source): You can put this solution on YOUR website!How do you simplify (3+i)^57 ----- 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 ---------------------------------- Form: (a+bi)^57 = r^57(cos(57(theta)) + i sin(57(theta)) ------------------------------------- (3+i)^57 = [sqrt(10)]^57[cos(57(18.43) + i sin(57(18.43)) = 3.1634x10^28(0.874416 - 049227i) ======================================= Cheers, Stan H.