Question

Find the product, (z1*z2)
and the quotient (z1/z2). Express your answers in polar form. (Express θ in radians.) z1 = cos π/4+ i sin π/4
z2 = cos 3π/4+ i sin 3π/4

Answer 1

z1 = cis pi/4
z2 = cis 3pi/4

z1*z2 = r1r2 cis angle1+angle2
= 1*1 cis 3+1 pi/4
= 1 cis pi
z1/z2 = r1/r2 cis angle1-angle2
= 1/1 cis 1-3 pi/4
= 1 cis -pi/2

Answer 2

thanks for the quick reply. But what is "cis"?

Answer 3

cis is short-hand for cos + i sin. r cis theta = r cos theta + i r sin theta

Answer 4

oh OK. thank you for the help!