Express the following in the form a +bi, where a and b are real numbers:
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Another accepted answer is -5-i, but if your teacher wants only one answer, then I'd go for 5+i

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Work Shown:

Equating terms, we have this system

Solve the second equation for b to get b = 5/a

Plug that into the first equation to solve for 'a'

Setting each factor equal to zero would lead to...

We're told that 'a' is a real number, so we ignore the solutions "a = i and a = -i". The only possible solutions are a = 5 and a = -5

If a = 5, then,

b = 5/a = 5/5 = 1

So

or in short,

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If a = -5, then b = 5/a = 5/(-5) = -1

So it's very possible that we could also say

If you wanted to combine the two we would use the plus/minus notation like so

This is due to (5+i)^2 and (-5-i)^2 both having the same result of 24+10i. Hence the plus/minus. If your teacher wants one answer only, then I'd go for 5+i, as we could consider it a "principal" square root in a sense.