2 (Complex Conjugation) Consider a complex number w = x +jy, having real part

Transcribed Image Text: Problem 1.2 (Complex Conjugation) Consider a complex number w = x +jy, having real part
Re(w) = x and imaginary part Im (w) = y, with its complex conjugate defined as w* = x – jy.
(a) Derive complex conjugation in polar form.
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(b)
Prove that (i) Re(w) = 1/2 (w +w*) and (ii) Im (w) = , (w – w*)

(c) Prove that |w? = ww* = |w*P, where |w| denotes the magnitude of w.
(d) Determine (i) Re(e” ) and (ii) Re(e”*).
(e) Determine (i) Im(e” ) and (ii) Im(e”* ).
(f) Sketch the complex plane (i) the solution to |w – j2| = 2 and (ii) the solution to |w* – j2| = 2.
Which number(s) are common to both solutions?

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