Algebra Examples

Find All Complex Number Solutions z=9+3i
Step 1
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
Step 2
The modulus of a complex number is the distance from the origin on the complex plane.
where
Step 3
Substitute the actual values of and .
Step 4
Find .
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Step 4.1
Raise to the power of .
Step 4.2
Raise to the power of .
Step 4.3
Add and .
Step 4.4
Rewrite as .
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Step 4.4.1
Factor out of .
Step 4.4.2
Rewrite as .
Step 4.5
Pull terms out from under the radical.
Step 5
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Step 6
Since inverse tangent of produces an angle in the first quadrant, the value of the angle is .
Step 7
Substitute the values of and .
Step 8
Replace the right side of the equation with the trigonometric form.
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