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Integral e^(1+i)x dx and roots of 1 and (1+i)

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(1) Find the indicated roots: (a) The eighth roots of 1 and (b) The cube roots fo 1+ i

(2) By considering the real and imaginary parts of the integral in part (1), evaluate the integral e^(1+i)x dx.

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Step by step solution is provided in detail. Integral functions and roots are determined. The real and imaginary parts are evaluated.

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1. Find the indicated roots. Sketch the roots in the complex plane.

We can write ' one' as follows since cos 2pi = 1 and sin 2pi = 0

1 = cos (2pi) + i sin (2pi)

In polar form this is written as follows:

1 = e i (2pi)

Take the eighth power in both ...

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