Question

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

Answer 1

Answer: it’s 3+i/10

Explanation:

i guessed on the answer above mine on the test and was correct

Answer 2

Comment
I'm taking this to mean

`( √(-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

`(i)/(1 + 3i)`

Step 4
Rationalize the denominator. Multiply top and bottom by (1 - 3i)

`(i * (1 - 3i))/((1 - 3i)(1 + 3i))`

Step 5
Simplify the denominator.


`(i*(1 - 3i))/((1 - 9i^2))`

`(i* (1 - 3i))/(1 + 9) = (i*(1 - 3i))/(10)`

Step Six
Remove the brackets in the numerator.

`(i + 4)/(10)\text{ I'll leave you to figure out the numerator}`