Solve 3/5-3i/5/sqrt{2}

$$\frac { \frac { 3 } { 5 } - \frac { 3 i } { 5 } } { \sqrt { 2 } }$$

Evaluate

$$\sqrt{2}\left(\frac{3}{10}-\frac{3}{10}i\right)\approx 0.424264069-0.424264069i$$

Solution Steps

Divide 3i by 5 to get \frac{3}{5}i.

$$\frac{\frac{3}{5}-\frac{3}{5}i}{\sqrt{2}}$$

Rationalize the denominator of \frac{\frac{3}{5}-\frac{3}{5}i}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(\frac{3}{5}-\frac{3}{5}i\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(\frac{3}{5}-\frac{3}{5}i\right)\sqrt{2}}{2}$$

Divide \left(\frac{3}{5}-\frac{3}{5}i\right)\sqrt{2} by 2 to get \left(\frac{3}{10}-\frac{3}{10}i\right)\sqrt{2}.

$$\left(\frac{3}{10}-\frac{3}{10}i\right)\sqrt{2}$$

Real Part

$$\frac{3 \sqrt{2}}{10} = 0.42426406871192857$$