Solve 1+i/-2i

$$\frac { 1 + i } { - 2 i }$$

Evaluate

$$-\frac{1}{2}+\frac{1}{2}i=-0.5+0.5i$$

Solution Steps

Multiply both numerator and denominator by imaginary unit i.

$$\frac{\left(1+i\right)i}{-2i^{2}}$$

By definition, i^{2} is -1. Calculate the denominator.

$$\frac{\left(1+i\right)i}{2}$$

Multiply 1+i times i.

$$\frac{i+i^{2}}{2}$$

By definition, i^{2} is -1.

$$\frac{i-1}{2}$$

Reorder the terms.

$$\frac{-1+i}{2}$$

Divide -1+i by 2 to get -\frac{1}{2}+\frac{1}{2}i.

$$-\frac{1}{2}+\frac{1}{2}i$$

Real Part

$$-\frac{1}{2} = -0.5$$

Solution Steps

Multiply both numerator and denominator of \frac{1+i}{-2i} by imaginary unit i.

$$Re(\frac{\left(1+i\right)i}{-2i^{2}})$$

By definition, i^{2} is -1. Calculate the denominator.

$$Re(\frac{\left(1+i\right)i}{2})$$

Multiply 1+i times i.

$$Re(\frac{i+i^{2}}{2})$$

By definition, i^{2} is -1.

$$Re(\frac{i-1}{2})$$

Reorder the terms.

$$Re(\frac{-1+i}{2})$$

Divide -1+i by 2 to get -\frac{1}{2}+\frac{1}{2}i.

$$Re(-\frac{1}{2}+\frac{1}{2}i)$$

The real part of -\frac{1}{2}+\frac{1}{2}i is -\frac{1}{2}.

$$-\frac{1}{2}$$