Question

Determine in which quadrant the product of cos 3pi/4 + isin 3pi/4 and 4(cos pi/2 + isin pi/2) lies.

Answer 1

The correct answer is quadrant three (QIII). Hope this helps!

Answer 2

III quadrant

Explanation:

Given are two complex numbers as

`z1=cos (3\pi )/(4)  + isin(3\pi )/(4)\\z2=cos (\pi )/(2)  + isin(\pi )/(2)`

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.