Question

Find the product of the complex numbers. Express your answer in trigonometry form. Z1= 7cos(15) + isin(15)) z2= 2(cos(110)+ isin(110))

Answer 1

14(cos(125°) +i·sin(125°))

Explanation:

The product of two complex numbers is the product of their magnitudes at an angle equal to the sum of their angles.

Application

For A = a·cis(α) and B = b·cis(β), the product AB is ...

AB = (a·cis(α))·(b·cis(β)) = ab·cis(α+β)

where "cis(x)" stands for the sum (cos(x) +i·sin(x)).

The product of interest is ...

Z1·Z2 = (7cis(15°))·(2cis(110°)) = (7·2)cis(15°+110°)

Z1·Z2 = 14cis(125°) = 14(cos(125°) +i·sin(125°))