What are the values of z1*z2 and z1/z2 if z1=27-13i, z2=18+7i given that they are used in trigonometric theorems?

We have the complex numbers z1 = 27 - 13i and z2 = 18 +
7i

z1*z2 = (27 - 13i)(18 + 7i)

open the
brackets and multiply

=> 27*18 + 27*7i - 13*18i -
13*7i^2

simplify noting that i^2 =
1

=> 486 + 189i - 234i +
91

=> 577 -
45i

z1/z2

=> (27 - 13i)/(18 +
7i)

multiply the numerator and denominator by (18 -
7i)

=> (27 - 13i)(18 - 7i)/(18 + 7i)(18 -
7i)

=> (27 - 13i)(18 - 7i)/(18^2 +
7^2)

=> (27*18 - 13*18i - 27*7i +
13*7i^2)/373

=> 395/373 -
(423/373)i

The value of z1*z2 = 577 - 45i and z1/z2 =
395/373 - (423/373)i