Let z1 4cos 300 i sin 300 and zz 16 cos 210 i sin 210 perfor

Let z1 4(cos 300+ i sin 300°) and zz 16 (cos 210+ i sin 210°); perform computations in polar exponential form; write EXACT answers in rectangular form. 3 Points each) a. 22 C. b. 2

Solution

a) z₁z₂ = 4 x 16(cos(300+210)^o + isin(300+210)^o) = 64(cos510^o+isin510^o) = 64(cos150^o+i sin150^o)= -55.4256 + 32i

b) z₁/z₂ = (4/16)(cos(300 - 210)^o + isin(300 - 210)^o) = 0.25(cos90^o + isin90^o) = 0.25i

c) (z₁)⁵ = (4)⁵(cos(5 x 300)^o + isin(5 x 300)^o) = 1024(cos1500^o + isin1500^o) = 512 + 886.81i