Question

please help me The question involves multiplying two complex numbers, then turning it into an a+bi equation (pictures included)

Answer 1

(a, b) = (0, -15)

Explanation:

In "cis" form the product of two complex numbers is the product of their magnitudes at the angle that is the sum of their angles. I find this the easiest way to multiply complex numbers.

z1 × z2 = (3 cis π)(5 cis π/2)

= (3·5) cis (π +π/2)

= 15 cis 3π/2

Of course, "cis" is short for "cosine + i·sine", so you have ...

z1 × z2 = 15 cis 3π/2 = 15(cos(3π/2) +i·sin(3π/2))

= 15(0 +i·(-1))

= 0 -15i

(a, b) = (0, -15)