SOLUTION: The complex number 13 + i can be factored into the product of 1 + 2i and what other complex number?

Question 192058: The complex number 13 + i can be factored into the product of 1 + 2i and what other complex number?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since 13 + i can be factored where one factor is , this means that

where "x" is the other factor

Start with the given equation.

Divide both sides by

Rearrange the equation

So the other factor is . Let's simplify

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Start with the given expression.

Multiply the fraction by .

Combine the fractions.

FOIL the numerator.

FOIL the denominator.

Multiply.

Combine like terms.

Break up the fraction.

Reduce.

So .

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Since , this means that

So the other factor is

So this means that

Note: you can check this by multiplying the given factor by to get

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