Answer:
III quadrant
Step-by-step explanation:
Given are two complex numbers as
[tex]z1=cos \frac{3\pi }{4} + isin\frac{3\pi }{4}\\z2=cos \frac{\pi }{2} + isin\frac{\pi }{2}[/tex]
Recall Demoivre theorem as
(cosA+isinA)(cos A+isin B) = cos(A+B)+isin(A+B)
Hence here we have product as
A+B = 3pi/4+pi/2
= 5pi/4
cos 5pi/4+isin 5pi/4 will be the product
Since 5pi/4 lies between pi and 3pi/2, we find that this lies in III quadrant.
