Solve frac{5texttt{i}}{5}*(10/3+10/3texttt{i})

$$\frac{ 5 \texttt{i} }{ 5 } \times ( \frac{ 10 }{ 3 } + \frac{ 10 }{ 3 } \texttt{i} )$$

Evaluate

$$-\frac{10}{3}+\frac{10}{3}i\approx -3.333333333+3.333333333i$$

Solution Steps

Divide 5i by 5 to get i.

$$i\left(\frac{10}{3}+\frac{10}{3}i\right)$$

Multiply i times \frac{10}{3}+\frac{10}{3}i.

$$\frac{10}{3}i+\frac{10}{3}i^{2}$$

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

$$\frac{10}{3}i+\frac{10}{3}\left(-1\right)$$

Do the multiplications. Reorder the terms.

$$-\frac{10}{3}+\frac{10}{3}i$$

Real Part

$$-\frac{10}{3} = -3\frac{1}{3} = -3.3333333333333335$$

Solution Steps

Divide 5i by 5 to get i.

$$Re(i\left(\frac{10}{3}+\frac{10}{3}i\right))$$

Multiply i times \frac{10}{3}+\frac{10}{3}i.

$$Re(\frac{10}{3}i+\frac{10}{3}i^{2})$$

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

$$Re(\frac{10}{3}i+\frac{10}{3}\left(-1\right))$$

Do the multiplications in \frac{10}{3}i+\frac{10}{3}\left(-1\right). Reorder the terms.

$$Re(-\frac{10}{3}+\frac{10}{3}i)$$

The real part of -\frac{10}{3}+\frac{10}{3}i is -\frac{10}{3}.

$$-\frac{10}{3}$$