Trigonometry Examples

Convert to Trigonometric Form (1+i)^3
Step 1
Use the Binomial Theorem.
Step 2
Simplify terms.
Tap for more steps...
Step 2.1
Simplify each term.
Tap for more steps...
Step 2.1.1
One to any power is one.
Step 2.1.2
One to any power is one.
Step 2.1.3
Multiply by .
Step 2.1.4
Multiply by .
Step 2.1.5
Rewrite as .
Step 2.1.6
Multiply by .
Step 2.1.7
Factor out .
Step 2.1.8
Rewrite as .
Step 2.1.9
Rewrite as .
Step 2.2
Simplify by adding terms.
Tap for more steps...
Step 2.2.1
Subtract from .
Step 2.2.2
Subtract from .
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
Find .
Tap for more steps...
Step 6.1
Raise to the power of .
Step 6.2
Raise to the power of .
Step 6.3
Add and .
Step 6.4
Rewrite as .
Tap for more steps...
Step 6.4.1
Factor out of .
Step 6.4.2
Rewrite as .
Step 6.5
Pull terms out from under the radical.
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 second quadrant, the value of the angle is .
Step 9
Substitute the values of and .