Question

Simplify the expression square root of -1 over (3+8i)-(2+5i)

Answer 1

Comment
I'm taking this to mean
$\frac{ \sqrt{-1} }{(3 + 8i) - (2 + 5i)}$

Step One
Simplify the denominator
3 + 8i - 2 - 5i
1 + 3i

Step Two
rewrite the numerator in terms of i.
sqrt(-1) = i

Step 3
rewrite the fraction
$\frac{i}{1 + 3i}$

Step 4
Rationalize the denominator. Multiply top and bottom by (1 - 3i)
$\frac{i * (1 - 3i)}{(1 - 3i)(1 + 3i)}$

Step 5
Simplify the denominator.

$\frac{i*(1 - 3i)}{(1 - 9i^2)}$
$\frac{i* (1 - 3i)}{1 + 9} = \frac{i*(1 - 3i)}{10}$

Step Six
Remove the brackets in the numerator.
$\frac{i + 4}{10}\text{ I'll leave you to figure out the numerator}$