SOLUTION: Convert -√3- i to polar form thanks in advance for helping me

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Question 1172294: Convert -√3- i to polar form
thanks in advance for helping me

Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


If , then where and .

For your problem, and .

Hint: , which is to say "the angle whose tangent is "

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.

The polar form is  -sqrt%283%29+-+i = r * ( cos(a) + i*sin(a) ),

where "r" is the polar radius and "a" is the polar angle.
.


So, our goal is to find the polar radius r and the polar angle "a".



    r = sqrt%28x%5E2+%2B+y%5E2%29 = sqrt%28%28-sqrt%28%283%29%29%5E2+%2B+%28-i%29%5E2%29%29 = sqrt%283%2B1%29 = sqrt%284%29+ = 2.


    tan(a) = y%2Fx = %28-1%29%2F%28-sqrt%283%29%29 = 1%2Fsqrt%283%29 = sqrt%283%29%2F3.



Therefore,  a = 7pi%2F6    ( taking into account that the angle "a" is in QIII ).



Thus the polar form is, finally,  -sqrt%283%29+-+i = 2%2A%28cos%287pi%2F6%29+%2B+i%2Asin%287pi%2F6%29%29 = (2, 7pi%2F6) = 2%2Acis%287pi%2F6%29.    ANSWER

Solved.

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    - Complex numbers and arithmetical operations on them
    - Complex plane
    - Addition and subtraction of complex numbers in complex plane
    - Multiplication and division of complex numbers in complex plane
    - Raising a complex number to an integer power
    - How to take a root of a complex number
    - Solution of the quadratic equation with real coefficients on complex domain
    - How to take a square root of a complex number
    - Solution of the quadratic equation with complex coefficients on complex domain

    - Solved problems on taking roots of complex numbers
    - Solved problems on arithmetic operations on complex numbers
    - Solved problem on taking square root of complex number
    - Miscellaneous problems on complex numbers
    - Advanced problem on complex numbers
    - Solved problems on de'Moivre formula
    - Calculating the sum 1*sin(1°) + 2*sin(2°) + 3*sin(3°) + . . . + 180*sin(180°)
    - A curious example of an equation in complex numbers which HAS NO a solution
    - Solving one non-standard equation in complex numbers
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The referred lessons are the part of this online textbook under the topic  "Complex numbers".


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