Show that (a) log(i2) 2 log i when log z ln r i (r 0, 4 9 4) (b) log(i2) 2 log i when log z ln r i (r 0, 3 4 11 4)

Question: Show that (a) log(i2) = 2 log i when log z = ln r + i (r > 0, /4 < < 9/4); (b)

Show that
(a) log(i2) = 2 log i when log z = ln r + iθ (r > 0, π/4 < θ < 9π/4);
(b) log(i2) ≠ 2 log i when log z = ln r + iθ (r > 0, 3π/4 < θ < 11π/4).

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