Answer:
[tex]\frac{6}{25}[/tex] - [tex]\frac{8}{25}[/tex] i
Step-by-step explanation:
Assuming you mean
[tex]\frac{2i}{-4+3i}[/tex]
To simplify, rationalise the denominator
Multiply the numerator/ denominator by the conjugate of the denominator
The conjugate of - 4 + 3i is - 4 - 3i , then
= [tex]\frac{2i(-4-3i)}{(-4+3i)(-4-3i)}[/tex] ← expand numerator and denominator
= [tex]\frac{-8i-6i^2}{16-9i^2}[/tex] [ note that i² = - 1 ]
= [tex]\frac{-8i+6}{16+9}[/tex]
= [tex]\frac{6-8i}{25}[/tex]
= [tex]\frac{6}{25}[/tex] - [tex]\frac{8}{25}[/tex] i ← in standard form
