Question

In this problem z = (6+i5) e^(6i).

(a)What are r = |z| and θ = arg(z)? identify which 45-degree “pizza slice” your angle is in, if you divide the range -pi to +pi into 8 intervals of size pi/4.

(b) Find the two values of √z in polar form.

(c) Find all values of ln(z). How many are there

Answer 1

Z: 16+15) 61 il') 6+15 10.1155) = 2 = Vol.e il 5/6) to l 10) 0:1 z) = 6 0.org (2) 180 391.5 2 deg: 360 +39.52. dan (6 - 31,520 First pizza sliçe 1909 45 TT (Arg 30 52 = 2 = (501.e 1/3)] ST = (69)", 179) 1) en 2: Ln12) + (Ang 2 +001) , n. 0,4),47,42. In Z = ln (501) + i/31.52" +297 ln Z 1 In (61) + i til 31.51+2nn) There two valuer og ang 2 : 31.50', 341.52 ave In 2 1/2 ln (61) + 1/ 31.52° +2nn) ano and I