Question

simplify the expression
-5+i / 2i
show all steps

Answer 1

To simplify the expression (-5+i) / (2i), we can multiply the numerator and denominator by the conjugate of the denominator to eliminate the complex number from the denominator.

The conjugate of 2i is -2i.

Multiplying the numerator and denominator by -2i, we get:

((-5+i)*(-2i)) / ((2i)*(-2i))

Simplifying the numerator:
((-5+i)*(-2i)) = 10i - 2i^2

Since i^2 is equal to -1:
10i - 2i^2 = 10i - 2(-1) = 10i + 2

And simplifying the denominator:
((2i)*(-2i)) = -4i^2

Since i^2 is equal to -1:
-4i^2 = -4(-1) = 4

Putting it all together:
(10i + 2) / 4

We can further simplify the expression by dividing each term by 2:
10i/4 + 2/4

Simplifying:
2.5i + 0.5i

Combining like terms:
3i