Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Fully simplify the expression 3−2i/5i
To simplify the expression (3-2i)/5i, we can multiply the numerator and denominator by -i to eliminate the complex number in the denominator.
(3-2i)/5i = (3-2i)/5i * -i/-i
Multiplying the numerator and denominator by -i gives us:
(3-2i)(-i)/5i(-i)
Distributing the -i to both terms in the numerator:
-3i + 2i^2 / -5i^2
Simplifying i^2 to -1:
-3i + 2(-1) / -5(-1)
-3i - 2 / 5
Combining like terms in the numerator:
(-2-3i) / 5
So the fully simplified expression is (-2-3i)/5.