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Trigonometry Examples
Step 1
Step 1.1
Factor out .
Step 1.2
Rewrite as .
Step 2
Step 2.1
Rewrite as .
Step 2.2
Rewrite as .
Step 2.3
Raise to the power of .
Step 3
One to any power is one.
Step 4
Multiply by .
Step 5
Rewrite as .
Step 6
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
Step 7
The modulus of a complex number is the distance from the origin on the complex plane.
where
Step 8
Substitute the actual values of and .
Step 9
Step 9.1
Raising to any positive power yields .
Step 9.2
Raise to the power of .
Step 9.3
Add and .
Step 9.4
Any root of is .
Step 10
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Step 11
Since inverse tangent of produces an angle in the second quadrant, the value of the angle is .
Step 12
Substitute the values of and .