20 POINTS Using mathematically precise language, explain in detail how you would multiply the complex number
z1=r1 (cos theta1+isin theta 1)
with the complex number
z2=r2 (cos theta 2+isin theta 2)

r-radius/radii
m-modulus/moduli
theta-argument represent angle theta

PRODUCT OF 2 COMPLEX NUMBERS: z1z2 = r1r2[cos (θ1+θ2) + isin (θ1+θ2)]

proof: r1(cos θ1 + isin θ1) × r2(cos θ2 + isin θ2)

= r1r2(cos θ1 + isin θ1) (cos θ2 + isin θ2)

= r1r2(cos θ1 cos θ2 + i cos θ1 sin θ2 + i sin θ1 cos θ2 + i2

sin θ1 sin θ2)

= r1r2(cos θ1 cos θ2 + i cos θ1 sin θ2 + i sin θ1 cos θ2 + (-1)sin θ1 sin θ2)

= r1r2(cos θ1 cos θ2 + i cos θ1 sin θ2 + i sin θ1 cos θ2 - sin θ1 sin θ2)

Step-by-step explanation:

when multipying these variables, you need to take into accound that the number has a value greater that its reciprical. useing an algebratic calculator can help. my tutor explained that to me. hope it helps :D