Solve 1+i/sqrt{-4}

$$\frac { 1 + i } { \sqrt { - 4 } }$$

Evaluate

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

Solution Steps

Calculate the square root of -4 and get 2i.

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

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

Calculate the square root of -4 and get 2i.

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

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}.

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