Solve (1-1/3)(-6/5+3i)

$$( 1 - \frac { 1 } { 3 } ) ( - \frac { 6 } { 5 } + 3 i )$$

Evaluate

$$-\frac{4}{5}+2i=-0.8+2i$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\left(\frac{3}{3}-\frac{1}{3}\right)\left(-\frac{6}{5}+3i\right)$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-1}{3}\left(-\frac{6}{5}+3i\right)$$

Subtract 1 from 3 to get 2.

$$\frac{2}{3}\left(-\frac{6}{5}+3i\right)$$

Multiply \frac{2}{3} times -\frac{6}{5}+3i.

$$\frac{2}{3}\left(-\frac{6}{5}\right)+\frac{2}{3}\times \left(3i\right)$$

Do the multiplications.

$$-\frac{4}{5}+2i$$

Real Part

$$-\frac{4}{5} = -0.8$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$Re(\left(\frac{3}{3}-\frac{1}{3}\right)\left(-\frac{6}{5}+3i\right))$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$Re(\frac{3-1}{3}\left(-\frac{6}{5}+3i\right))$$

Subtract 1 from 3 to get 2.

$$Re(\frac{2}{3}\left(-\frac{6}{5}+3i\right))$$

Multiply \frac{2}{3} times -\frac{6}{5}+3i.

$$Re(\frac{2}{3}\left(-\frac{6}{5}\right)+\frac{2}{3}\times \left(3i\right))$$

Do the multiplications in \frac{2}{3}\left(-\frac{6}{5}\right)+\frac{2}{3}\times \left(3i\right).

$$Re(-\frac{4}{5}+2i)$$

The real part of -\frac{4}{5}+2i is -\frac{4}{5}.

$$-\frac{4}{5}$$