Pre-Calculus: Find z * w and z/w

Question

Find z * w and z/w for problems a and b.

a) z=1-i ; w=1-sqrt(3)i

b) z=2(cos 2pi/9 + isin 2pi/9 )

w=4(cos pi/9 + isin pi/9)

Answer 1

a) z=1-i, w=1-isqr3

zw = (1-i)(1-isqr3) = 1 - sqr3 - (1+sqr3)i

zw = about -0.732 - 2.732i

z/w = (1-i)/(1-isqr3) = (1-i)(1+isq3)/(1-3) = (1+sqr3 -i +isqr3)/-2

z/w= about (2.732+.732)i/-2

z/w = about -1.366 - 0.366i