Question

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

Answer 1

Answer:

-10/3 is the answer

Step-by-step explanation:

Given are two complex numbers as

$z1=\frac{2}{5} (cos63 + isin63)\\z2=\frac{10}{3} (cos 117 + isin117})$

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

$z1z2=\frac{2}{5} \frac{10}{3} (cos180+isin180)$

=$\frac{-10}{3}$

Since sin180=0 and cos 180=-1