To simplify the expression (-5 + i) / (2i), we rationalize the denominator by multiplying both the numerator and denominator by -2i. After simplifying, the expression becomes (5i + 1) / (-2).
To simplify the expression (-5 + i) / (2i), we can rationalize the denominator.
Multiplying the numerator and denominator by the conjugate of the denominator will help eliminate the imaginary part in the denominator.
The conjugate of 2i is -2i, so we can multiply the numerator and denominator by -2i:
((-5 + i) / (2i)) * ((-2i) / (-2i))
Simplifying the numerator:
((-5 + i) * (-2i)) = (10i - 2i^2) = (10i + 2)
Simplifying the denominator:
(2i * (-2i)) = (4i^2) = (-4)
Putting it all together:
((-5 + i) / (2i)) * ((-2i) / (-2i)) = (10i + 2) / (-4)
We can further simplify the expression by dividing both the numerator and denominator by 2:
(10i + 2) / (-4) = (5i + 1) / (-2)
Therefore, the simplified expression is (5i + 1) / (-2).