Perform the indicated operation Give answers in rectangular

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. 50) (12 cis 14.5 degree)(3 cis 8.5 degree)

Solution

12cis14.5 /3cis8.5

write numerator and denomiantor in polar form

12cis14.5 = 12e^i(14.5)

3cis8.5 = 3e^i(8.5)

12cis14.5 /3cis8.5 =  12e^i(14.5)/ 3e^i(8.5)

= 4e^i6

= 4(cos6 +isin6)

= 3.9780 + i*0.4181