Write each complex number in rectangular form?

Question

I need help with this. :/

2(cos120°+i sin 120°)

and

4(cos 7π/4 + i sin 7π/4)

?

Answer 1

2*cos120 + i2*sin120.

X = hor = 2*cos120 = -1.
Y = VER = 2*sin120 = 1.732.

tanA = Y/X = 1.732/-1 = -1.732,
A = -60 deg = 300 deg CCW.

R = X/cosA = = -1/cos300 = -2 = Resultant.

R = -2 @ -60 deg = -2 @ 300 deg CCW.

4*cos7pi/4 + i4*sin7pi/4,

7pi/4 = 7*180/4 = 315 deg.
X = hor = 4*cos315 = 2.83.
Y = ver = 4*sin315 = -2.83.

tanA = Y/X = -2.83/2.83 = -1.
A = -45 deg = 315 deg CCW.

R = X/cosA = 2.83/cos315 = 4.0 = Resultant.

R = 4.0 @ -45 deg = 4.0 @ 315 deg CCW = Resultant.