SOLUTION: 1/2 √(|2-3i|+a)± i√(|2-3i| )-a

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Question 945908: 1/2 √(|2-3i|+a)± i√(|2-3i| )-a
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This includes finding the size of a complex number. Maybe easier to do that first.

abs%282-3i%29=sqrt%282%5E2%2B3%5E2%29=sqrt%284%2B9%29=sqrt%2813%29

Revise original expression:

%281%2F2%29sqrt%28sqrt%2813%29%2Ba%29%2B-+%28i%2Asqrt%28sqrt%2813%29%29-a%29

sqrt%28sqrt%2813%29%2Ba%29%2F2%2B-+%28i%2Asqrt%28sqrt%2813%29-a%29

sqrt%28sqrt%2813%29%2Ba%29%2F2%2Bi%2Asqrt%28sqrt%2813%29%29-a
OR
sqrt%28sqrt%2813%29%2Ba%29%2F2-i%2Asqrt%28sqrt%2813%29%29%2Ba

Putting into better complex number form,
%28sqrt%28sqrt%2813%29%2Ba-2a%29%2F2%2Bi%2Asqrt%28sqrt%2813%29%29
OR
%28sqrt%28sqrt%2813%29%2Ba%2B2a%29%2F2-i%2Asqrt%28sqrt%2813%29%29

Finally:
highlight%28%28sqrt%28sqrt%2813%29-a%29%2F2%2Bi%2Asqrt%28sqrt%2813%29%29%29
OR
highlight%28%28sqrt%28sqrt%2813%29%2B3a%29%2F2-i%2Asqrt%28sqrt%2813%29%29%29

(Look at the text under the failed-renduring to see clearly.)