Solve 6i(2/5+6/5i)

$$6 i ( \frac { 2 } { 5 } + \frac { 6 } { 5 } i )$$

Evaluate

$$-\frac{36}{5}+\frac{12}{5}i=-7.2+2.4i$$

Solution Steps

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

$$6i\times \frac{2}{5}+6\times \frac{6}{5}i^{2}$$

By definition, i^{2} is -1.

$$6i\times \frac{2}{5}+6\times \frac{6}{5}\left(-1\right)$$

Do the multiplications. Reorder the terms.

$$-\frac{36}{5}+\frac{12}{5}i$$

Real Part

$$-\frac{36}{5} = -7\frac{1}{5} = -7.2$$

Solution Steps

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

$$Re(6i\times \frac{2}{5}+6\times \frac{6}{5}i^{2})$$

By definition, i^{2} is -1.

$$Re(6i\times \frac{2}{5}+6\times \frac{6}{5}\left(-1\right))$$

Do the multiplications in 6i\times \frac{2}{5}+6\times \frac{6}{5}\left(-1\right). Reorder the terms.

$$Re(-\frac{36}{5}+\frac{12}{5}i)$$

The real part of -\frac{36}{5}+\frac{12}{5}i is -\frac{36}{5}.

$$-\frac{36}{5}$$