SOLUTION: Write the complex number z = -6 -2i in trigonometric form (sometimes called polar form). Express the angle &#952; in radians, where 0 <= &#952; < 2 pi Z = ___(cos___ + i sin __

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Write the complex number z = -6 -2i in trigonometric form (sometimes called polar form). Express the angle &#952; in radians, where 0 <= &#952; < 2 pi Z = ___(cos___ + i sin __      Log On


   



Question 1070700: Write the complex number z = -6 -2i in trigonometric form (sometimes called polar form). Express the angle θ in radians, where 0 <= θ < 2 pi
Z = ___(cos___ + i sin ____)
I greatly appreciate an answer to this question.
The answer I am getting is:
r = 6.32456
θ = -161.565 Degrees
But i do not know how to put it in cosine + i sin form.

Z = ___(cos___ + i sin ____)

Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Your answer is partially correct.
Your angle should be in radians and not degrees.
2pi=360 is the conversion from radians to degrees.
Also,the angle needs to be between (0,2pi).
You need to add 2pi radians or 360 degrees.
theta=%28-161.565%2B360%29%2A%28%282pi%29%2F360%29=3.46radians
.
.
.
Also, you can keep the radical form and then there's no need for approximations,
highlight%28Z=2sqrt%2810%29%2A%28cos%283.46%29%2Bi%2Asin%283.46%29%29%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write the complex number z = -6 -2i in trigonometric form (sometimes called polar form). Express the angle θ in radians, where 0 <= θ < 2 pi
-----------
r = 2sqrt(10) (as you stated)
Theta = atan(-2/-6) =~ 198.43º
Theta = 3.46 radians
=====================
z = 2sqrt(10)cis(theta)
= 2sqrt%2810%29%28cos%28theta%29+%2B+isin%28theta%29%29
= 2sqrt%2810%29%28cos%283.46%29+%2B+isin%283.46%29%29