Solve for α
\alpha =-2
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1+i=\frac{1}{2}i\left(i\alpha +2\right)
Variable \alpha cannot be equal to 2i since division by zero is not defined. Multiply both sides of the equation by i\alpha +2.
1+i=-\frac{1}{2}\alpha +i
Use the distributive property to multiply \frac{1}{2}i by i\alpha +2.
-\frac{1}{2}\alpha +i=1+i
Swap sides so that all variable terms are on the left hand side.
-\frac{1}{2}\alpha =1+i-i
Subtract i from both sides.
-\frac{1}{2}\alpha =1
Subtract i from 1+i to get 1.
\alpha =1\left(-2\right)
Multiply both sides by -2, the reciprocal of -\frac{1}{2}.
\alpha =-2
Multiply 1 and -2 to get -2.
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