Question

Find z1z2 if z1 = 2/5(cos63° + isin63°) and z2 = 10/3(cos117° + isin117°).

Answer 1

-4/3

Explanation:

Took the quiz on odyssey ware and got it right

Answer 2

-10/3 is the answer

Explanation:

Given are two complex numbers as

`z1=(2)/(5) (cos63  + isin63)\\z2=(10)/(3) (cos 117 + isin117})`

Recall Demoivre theorem as

(cosA+isinA)(cos A+isin B) = cos(A+B)+isin(A+B)

Hence here we have sum of angles as

A+B = 63+117 =180

`z1z2=(2)/(5) (10)/(3) (cos180+isin180)`

=
`(-10)/(3)`

Since sin180=0 and cos 180=-1