[100 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)
Multiply the moduli and add the arguments.Step-by-step explanation:First write out the two terms being multiplied: z1z2= [r1(cos(theta 1) + isin(theta 1))][r2(cos(theta 2)+ isin(theta 2))] z1z2= r1r2 (cos(theta 1) + isin(theta 1))(cos(theta 2)+ isin(theta 2)) z1z2= r1r2(cos(theta 1)cos(theta 2))+(icos(theta 1)sin(theta 2))+(icos(theta 2)sin(theta 1))+(i^2 sin(theta 1)sin(theta 2)) Next group and rewrite the like term with the sums and differences. Your answer is the multiplication of the moduli and the addition of the arguments: z1z2= r1r2[cos(theta 1 + theta 2) + i sin (theta 1 and theta 2)].
