Perform the operation and leave the result in trigonometric

Perform the operation and leave the result in trigonometric form (let 0 lessthanorequalto theta lessthanorequalto 2pi 5cos(3.7) + i sin (3.7))/4(cos(1.6) + i sin (1.6)) Perform the operation and leave the result in trigonometric form cos(7pi/4 + i sin (7pi/4/cos pi + i sin pi

Solution

5(cos(3.7) +isin(3.7))/4( cos1.6 +isin1.6)

=5e^(3.7i)/4e^(1.6i)    ( Euler\'s form)

= 1.2e^(3.7 -1.6)i

= 1.2e^2.1i

= 1.2(cos2.1 + i*sin2.1)

[ cos(7pi/4) + isin(7pi/4)]/[ cospi +isinpi]

cospi = -1 ; sinpi = 0

So, [ cos(7pi/4) + isin(7pi/4)]/[ cospi +isinpi]

= - cos(7pi/4) - i*sin(7pi/4)