Question 37560
2i+3/4-i + 1-i/4+i 

One fraction at a time:
1st:
(2i+3)/(4-i)
Multiply numerator and denominator by (4+i) to get:
[(2i+3)(4+i)]/[16+1]=[12-2+11i]/17=[10+11i]/17

2nd:
Multiply num and denom by 4-1 to get:
[(1-i)(4-i)]/17= [(4-1)-5i]/17=[3-5i]/17

Adding 1st and 2nd you get:
[13+6i]/17

Cheers,
Stan H.