How do I simplify this?

Question

-5+i/2i

I have been having trouble with the imaginary number concept and would like some help with this question. Thanks so much!

Answer 1

Multiply the numerator and denominator by the conjugate of the denominator to find

2
+
i
1
−
i
=
1
2
+
3
2
i

Explanation:
The conjugate of a complex number
a
+
b
i
is
a
−
b
i
. The product of a complex number and its conjugate is a real number. We will use this fact to eliminate the complex number from the denominator of the given expression.

2
+
i
1
−
i
=
(
2
+
i
)
(
1
+
i
)
(
1
−
i
)
(
1
+
i
)

=
2
+
2
i
+
i
−
1
1
+
i
−
i
+
1

=
1
+
3
i
2

=
1
2
+
3
2
i

Answer 2

sorry the numbers got messed up

Answer 3

All good! Thank you so much! You are very helpful!!

Answer 4

since i^2 = -1,
1/i = -i
so (-5+i)/(2i) = (-5+i)(-i/2) = 1/2 + 5/2 i
or, using the conjugate,
(-5+i)/(0+2i) = (-5+i)(0-2i)/(0^2+2^2) = (-5+i)(-2i)/4 = 1/2 + 5/2 i