SOLUTION: express in polar form, using the smallest non-negative value for the argument. -1/2 + radical 3/2 i

Question 384770: express in polar form, using the smallest non-negative value for the argument.
-1/2 + radical 3/2 i
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
express in polar form, using the smallest non-negative value for the argument.
-1/2 + radical 3/2 i
-----------------
r = sqrt[(1/2)^2 + (sqrt(3)/2)^2] = sqrt[1/4 + 3/4] = 1
-------
theta = arctan[(sqrt(3)/2)/(1/2)] = arctan[sqrt(3)] = 60 degrees
--
But the point is in the 2nd Quadrant so theta = 120 degrees or (2pi/3)
---
Polar Form: 1(cos(2pi/3)+isin(2pi/3))
============================
Cheers,
Stan H.
RELATED QUESTIONS
Express 2 - 2i in polar form using principal... (answered by MathLover1)

Express -1 + √3i in polar form using principal... (answered by ikleyn)

Please help. I do not understand Write the complex number in rectangular form. 1.)... (answered by Edwin McCravy)

Solve for the smallest non-negative value of �: Square root of... (answered by ikleyn)

Convert the given coordinates to the equivalent polar form: (negative radical 2, negative (answered by fractalier)

Write the complex number in polar form with argument θ between 0 and 2π.... (answered by ikleyn)

Solve for x using the quadratic formula. Express your answer in the simplest radical... (answered by josgarithmetic)

Solve for x using the quadratic formula. Express your answer in simplest radical form: (answered by josgarithmetic)

Plot this complex number in the complex plane and write it in polar form. Express the... (answered by Fombitz)