Math & Physics Problems Wikia
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Problem

Use complex variables to compute and simultaneously.

Argand-plane.png

Remark: This exercise saves a lot of work!

Solution

Consider the integral

.

Since ,

.

Multiply the numerator and denominator by the complex conjugate on the right hand side.

.

By matching real terms and complex terms, and tacking on the arbitrary constant from integrating, we can conclude that

and

.
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