fully simplify the expression
3-2i/5i
show all work
To fully simplify the expression `(3 - 2i) / (5i)`, we can eliminate the complex number in the denominator by multiplying the numerator and denominator by `i`:
`(3 - 2i) / (5i)` * `(i) / (i)`
Multiplying the denominators together, we get:
`(3 - 2i)(i) / (5i)(i)`
Expanding the numerator and denominator, we have:
`(3i - 2i^2) / (5i^2)`
Since `i^2 = -1`, this simplifies to:
`(3i + 2) / (-5)`
Inverting the denominator to change the division to multiplication, we get:
`(3i + 2) * (-1/5)`
Distributing the `-1/5` to the terms in the numerator, we have:
`(-3i/5) - (2/5)`
So the fully simplified expression is `-3i/5 - 2/5`.