Taking big powers of complex numbers | Analysis | Math2Go

In this video we will show how you can take big powers of complex numbers. This principle applies to many other similar problems as well!

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[Robert_H.]

1 + i = sqrt(2) e^((i π)/4)

(1 + i)^40 = (sqrt(2))^40 * (e^((i π)/4))^40 = 2^20 * e^(i 10π) = 2^20 = 1.048.576