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Fully simplify the expression
3−2i/5i
To simplify the expression (3 - 2i) / 5i, we can multiply the numerator and denominator by the conjugate of the denominator to eliminate the complex number in the denominator.
The conjugate of 5i is -5i.
So, multiplying the numerator and denominator by -5i, we have:
[(3 - 2i) / 5i] * [-5i / -5i]
Simplifying the numerator and denominator separately, we get:
(3 * -5i - 2i * -5i) / (5i * -5i)
= (-15i + 10i²) / (-25i²)
= (-15i + 10(-1)) / (-25(-1))
= (-15i - 10) / 25
= -15i / 25 - 10 / 25
= -3i / 5 - 2 / 5
Therefore, the fully simplified expression is: -3i/5 - 2/5.