Linear Algebra Examples

Convert to Trigonometric Form (5i)(2+6i)
Step 1
Apply the distributive property.
Step 2
Multiply by .
Step 3
Multiply .
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Step 3.1
Multiply by .
Step 3.2
Raise to the power of .
Step 3.3
Raise to the power of .
Step 3.4
Use the power rule to combine exponents.
Step 3.5
Add and .
Step 4
Simplify each term.
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Step 4.1
Rewrite as .
Step 4.2
Multiply by .
Step 5
Reorder and .
Step 6
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
Step 7
The modulus of a complex number is the distance from the origin on the complex plane.
where
Step 8
Substitute the actual values of and .
Step 9
Find .
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Step 9.1
Raise to the power of .
Step 9.2
Raise to the power of .
Step 9.3
Add and .
Step 9.4
Rewrite as .
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Step 9.4.1
Factor out of .
Step 9.4.2
Rewrite as .
Step 9.5
Pull terms out from under the radical.
Step 10
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Step 11
Since inverse tangent of produces an angle in the second quadrant, the value of the angle is .
Step 12
Substitute the values of and .