Question

[4] Convert z = -10 and w = -13 + i tor cis O form and then find zw. 2, and w*. Leave answers in r cis form. Sketches have been provided on the scratchwork page. W ZW= z W W [5] Find zw, 2, and wgiven w = - 12 - i 2 and 2 = - 8i . Leave answers in r cis @ form. Sketches have been provided on the scratchwork page. W ZW= Z II w [6] Polar coordinates of a point are given. Find the rectangular coordinates of each point. Note: If 0 is a "special" angle, then the coordinates should be exact. Otherwise, round to the nearest tenth Sketches have been provided on the scratchwork page. -11, (7, 150) -14, 7 4 (3, 160°) [7] Rectangular coordinates of a point are given. Find the polar coordinates for each point such that r 20 and 0% 0<2n. Sketches have been provided on the scratchwork page. (-2, -213) (8.-8) (-1,0) (-24, 7)

Answer 1

Problem: 4 Z-10 w = -√3ti solution : z = -10 +0.1 on negatire n-amis. . Argument o =TI = VE 0202 = 100 = 10 By Demoirre's theorem z = -10toi &CCOBO+ isine) are - 10 (COBI + isnt) = to e =relo Similary: w==.&3 ti quadrant I Argument, o= II - tant ! -T-IL 6 = 51 6 VE 32+2 = √9+ = 54=2 W = 80080 +isino) = 2(6039 S +isin su) -20%

Now, STI 10 dit & a est xilo (+1+39) (1) 20 - 20e 7.W = 20 cis 110) EN So ein 12 SIT Zeist - sei (TT-ST) =seil EN 2 seis (!) w+- (20)24.10 ) = 16 e 101 W4 - 16 cis (103)