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When i punched it into a calculator, it told me it was 2+2i
in order to simplify this type of equations rationalizing the denominator allows to get a simple equation
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Here you need to get rid of i from the denominator. To do that, you need to multiply the denominator by its complex conjugate.
The complex conjugate of a + bi is a - bi
Since you are working with a fraction, whatever you multiply the denominator by, you must multiply the numerator by the same thing.
The complex conjugate of 1 + 5i is 1 - 5i
(1 - 5i)/(1 - 5i) = 1 becasue when you divide a number by itself (except 0) you get 1.
okay so 1 -8i?
So by multiplying your original fraction by (1 - 5i)/(1 - 5i) you are not changing the value, only the form.