Multiply the numerator and denominator by the conjugate of 2i to make the denominator a real number:
-5 + 1 / 2i
= -5 + i /2i x i/i
= -5i + i^2 / 2 x i^2
Rewrite i^2 as -1:
-5i + -1 / 2 x -1
Simplify:
= -1 - 5i / -2
Split the fraction into two separate ones:
1/2 + 5i/2
Explanation:
mutiply (-5+i) and 2i with 2i
2i × 2i = 4i^2 ➡-4
2i × (-5+i) = -10i + 2i^2 ➡-10i -2
then do the division
(-10i -2)/-4 = (5i + 1)/2
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