Find zw and zw Leave your answers in polar form z 6cos8i sin

Find zw and z/w

Leave your answers in polar form.

z =6(cos/8+i sin/8)

w=6(cos/12+i sin/12

What is the product?

(Simplify your answers. Use integers or fractions for any numbers in the expression. Type any angle measures in radians. Type exact answers, using as needed.)

What is the quotient?

Solution

z=6(cos pi/8 + i sin pi/8 ) =   6e^(i*pi/8)

w= 6(cos pi/12 + i sin pi/12)= 6e^(i*pi/12)

z*w=6e^(i*pi/8)* 6e^(i*pi/12)= 36e^(i*5pi/24)

36( cos 5pi/24+isin 5pi/24)

z/w= 6e^(i*pi/8)/6e^i(pi/12)= e^(i pi/8 - i pi/12 )= e^(i pi/24)

cos pi/24 + i sin pi/24