Convert to Trigonometric Form -( square root of 3)/2-1/2i

Math
Combine and .
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
The modulus of a complex number is the distance from the origin on the complex plane.
where
Substitute the actual values of and .
Find .
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Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Multiply by .
One to any power is one.
Raise to the power of .
Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Simplify the expression.
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Raise to the power of .
Multiply by .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
Simplify the expression.
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Raise to the power of .
Combine the numerators over the common denominator.
Add and .
Divide by .
Any root of is .
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Since inverse tangent of produces an angle in the third quadrant, the value of the angle is .
Substitute the values of and .
Convert to Trigonometric Form -( square root of 3)/2-1/2i


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