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Trigonometry Examples
Step 1
Step 1.1
Rewrite as .
Step 1.1.1
Factor out .
Step 1.1.2
Rewrite as .
Step 1.1.3
Factor out .
Step 1.2
Rewrite as .
Step 1.2.1
Rewrite as .
Step 1.2.2
Rewrite as .
Step 1.2.3
Raise to the power of .
Step 1.3
One to any power is one.
Step 1.4
Multiply by .
Step 1.5
Rewrite as .
Step 1.6
Rewrite as .
Step 1.7
Multiply by .
Step 1.8
Rewrite as .
Step 1.8.1
Factor out .
Step 1.8.2
Rewrite as .
Step 1.9
Rewrite as .
Step 1.9.1
Rewrite as .
Step 1.9.2
Rewrite as .
Step 1.9.3
Raise to the power of .
Step 1.10
One to any power is one.
Step 1.11
Multiply by .
Step 1.12
Rewrite as .
Step 1.13
Multiply by .
Step 2
Reorder and .
Step 3
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
Step 4
The modulus of a complex number is the distance from the origin on the complex plane.
where
Step 5
Substitute the actual values of and .
Step 6
Step 6.1
Raise to the power of .
Step 6.2
Raise to the power of .
Step 6.3
Add and .
Step 7
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Step 8
Since inverse tangent of produces an angle in the third quadrant, the value of the angle is .
Step 9
Substitute the values of and .