Question

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))

Answer 1

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