Write each complex number in rectangular form.

a. 2 (cos (135) + i sin (135))

b. 3 (cos (120)) + i sin (120))

c. 5 (cos (5pi/4) + i sin (5pi/4))

d. 4 (cos (5pi/3) + i sin (5pi/3))

Hello,

A)

cos 135° = - cos 45°=-√2/2

sin 135°=sin45°=√2/2

2 (cos 135°+i sin 135°) = - √2 + i*√2

B)

cos 120°=-cos 30°=-√3 / 2

sin 120°=sin 30°=1/2

3 (cos 120° + i sin 120) = - 3/2*√3 + i*3/2

C)

cos (5π/4) = - cos (π/4) = - √2 / 2

sin (5π/4) = - sin (π/4) = - √2 / 2

5 (cos (5π/4) + i sin (5π/4)) = - 5/2*√2 + i * 5/2*√2

D)

cos (5π/3) = cos (π/3) = √3 / 2

sin (5π/3) = - sin (π/3) = - 1/2

4 (cos (5pi/3) + i sin (5pi/3))

=2√3 - 2*i