Solve (frac{sqrt{46}i}{2})^2

$$( \frac { \sqrt { 46 } i } { 2 } ) ^ { 2 }$$

Evaluate

$$-\frac{23}{2}=-11.5$$

Solution Steps

Divide i\sqrt{46} by 2 to get \frac{1}{2}i\sqrt{46}.

$$\left(\frac{1}{2}i\sqrt{46}\right)^{2}$$

Expand \left(\frac{1}{2}i\sqrt{46}\right)^{2}.

$$\left(\frac{1}{2}i\right)^{2}\left(\sqrt{46}\right)^{2}$$

Calculate \frac{1}{2}i to the power of 2 and get -\frac{1}{4}.

$$-\frac{1}{4}\left(\sqrt{46}\right)^{2}$$

The square of \sqrt{46} is 46.

$$-\frac{1}{4}\times 46$$

Multiply -\frac{1}{4} and 46 to get -\frac{23}{2}.

$$-\frac{23}{2}$$

Real Part

$$-\frac{23}{2} = -11\frac{1}{2} = -11.5$$

Solution Steps

Divide i\sqrt{46} by 2 to get \frac{1}{2}i\sqrt{46}.

$$Re(\left(\frac{1}{2}i\sqrt{46}\right)^{2})$$

Expand \left(\frac{1}{2}i\sqrt{46}\right)^{2}.

$$Re(\left(\frac{1}{2}i\right)^{2}\left(\sqrt{46}\right)^{2})$$

Calculate \frac{1}{2}i to the power of 2 and get -\frac{1}{4}.

$$Re(-\frac{1}{4}\left(\sqrt{46}\right)^{2})$$

The square of \sqrt{46} is 46.

$$Re(-\frac{1}{4}\times 46)$$

Multiply -\frac{1}{4} and 46 to get -\frac{23}{2}.

$$Re(-\frac{23}{2})$$

The real part of -\frac{23}{2} is -\frac{23}{2}.

$$-\frac{23}{2}$$