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

If you can just give me the equation to turn a complex number into rectangular form, that would be much appreciated :)

Answer 2

There are two other ways of writing the polar form of a complex number:
r cis θ [means r (cos θ + j sin θ)]
r ∠ θ [means once again, r (cos θ + j sin θ)]
we can write the polar form of a complex number as:x + yj = r(cos θ + j sin θ)
a.2cos 135 + i (2sin 135) = -sqrt 2 + sqrt 2 i
b. 3(cos(120 degrees) + i sin(120 degrees)) = 3 cos 120 + i (3 sin 120) = -3/2 + 3/2sqrt3 i
c. 5(cos(5pi/4) + i sin(5pi/4)) = 5 ( - 1/2 * sqrt 2) +5.sqrt(2)/2 i = -5/2sqrt 2 + 5/2 sqrt 2 i
cos(5pi/4)= cos (pi + 1/4 pi)= cos pi * cos 1/4 pi - sin pi * sin 1/4pi= 0 * cos 1/4pi - 1 * sin 1/4 pi=-sin (pi/4)= - sin 45= - 1/2 * sqrt 2
sin(5pi/4) = -sqrt(2)/2
d. 4(cos(5pi/3) + i sin(5pi/3)) = 4 (cos 300) + 4 (sin 300) i = 4. 1/2 - 4. sqrt(3)/2 i = 2 - 2sqrt(3) i
5pi/3 = 300 degrees. cos 300 = cos 60 = 0.5
sin 300 = - sin 60 = -sqrt(3)/2

Answer 3

XD

Answer 4

Geeeeeeeze xD Thank you :)

Answer 5

you have the answer