SOLUTION: how do you solve: (1-4i)/(2+3i) i indicates a number that is imaginary ( sqrt of -1) thanks so much

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Question 582098: how do you solve: (1-4i)/(2+3i)

i indicates a number that is imaginary ( sqrt of -1)

thanks so much
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
how do you solve: (1-4i)/(2+3i)
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You don't solve it. There's no variable to solve for.
The goal is to rationalize the denominator, ie, get the i out of it.
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(1-4i)/(2+3i)
Multiply the NUM and DEN by the conjugate of the DEN, 2-3i
= (1-4i)(2-3i)/((2+3i)(2-3i))
= (2 - 11i +12i^2)/(4 - 9i^2)
= (2 - 11i - 12)/(4 + 9)
= (-10 - 11i)/13
or -10/13 - i(11/13)