Solve -9-9i/sqrt{2}

$$- \frac { 9 - 9 i } { \sqrt { 2 } }$$

Evaluate

$$\sqrt{2}\left(-\frac{9}{2}+\frac{9}{2}i\right)\approx -6.363961031+6.363961031i$$

Solution Steps

Rationalize the denominator of \frac{9-9i}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$-\frac{\left(9-9i\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-\frac{\left(9-9i\right)\sqrt{2}}{2}$$

Divide \left(9-9i\right)\sqrt{2} by 2 to get \left(\frac{9}{2}-\frac{9}{2}i\right)\sqrt{2}.

$$-\left(\frac{9}{2}-\frac{9}{2}i\right)\sqrt{2}$$

Multiply -1 and \frac{9}{2}-\frac{9}{2}i to get -\frac{9}{2}+\frac{9}{2}i.

$$\left(-\frac{9}{2}+\frac{9}{2}i\right)\sqrt{2}$$

Real Part

$$-\frac{9 \sqrt{2}}{2} = -6.3639610306789285$$