Please explain best method to solve these types of problems.

Question

Find 𝑧1𝑧2 in polar form where 𝑧1=7(cos(64∘)+𝑖sin(64∘)) and 𝑧2=3(cos(116∘)+𝑖sin(116∘)).

Answer 1

Recall that e^ix = cosx + i sinx

If you write z1 as 7e^64°i and z2 as 3e^116°i , their product is

21e^180°i =

21 * -1 =

-21

If you like, you could write e^180°i as cos180° + isin180° = -1 above.