Linear Algebra Examples

Convert to Trigonometric Form -4+0i
Step 1
Multiply by .
Step 2
Add 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
Find .
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Step 6.1
Raising to any positive power yields .
Step 6.2
Raise to the power of .
Step 6.3
Add and .
Step 6.4
Rewrite as .
Step 6.5
Pull terms out from under the radical, assuming positive real numbers.
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 .