Question

14 For the complex number z=-3+3i do the following a) Convert to polar form, Polar 2- b) Still in polar form, find z? Polar c) Finally convert z' back to standard form Standard 2' =

Answer 1

Givena Z = -3+3 i @ Polar form of z = x+iy is Z = [cos o risino] = x2 tyz where Y and 0 = tant Here z = - 3+ 3i 20= -37 y = 3 r= V1²+yz √(-3)²+ 2 g+g vis + 3 JIS 3 2 and taño (22) = taña = tañ' (-1) Z is Now, located the complex number = -3 +31 in the second quadrant. O- tan (-1) = 3T 4 polar form of z = - 3+37 is Za r [coso + isin o) = 3 v2 [cos (3) Z i sin (T)]

Now, Z Z = 312 [co cos (3) i sin (3) zi 7 (382) cos (2) + i sin (3) -1749663 [cos (SI)) + i sin (3)] - By Det moivres theorem, (coso+isino)" - Cosno +isin no . z? 21 TT Z 15496 r7 [cos (215 + i sin c 7 z 17496 r2 cos 21 4 i + 21 TT sin ( ²1 = 174962 - 174962 C- 1/5 i 고 17496 17496 i -