Linear Algebra Examples

Convert to Trigonometric Form (-7+4i)-(-9-3i)
Step 1
Simplify each term.
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Step 1.1
Apply the distributive property.
Step 1.2
Multiply by .
Step 1.3
Multiply by .
Step 2
Simplify by adding terms.
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Step 2.1
Add and .
Step 2.2
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
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 first quadrant, the value of the angle is .
Step 9
Substitute the values of and .