Solve frac{70-20texttt{i}}{0-10texttt{i}}

$$\frac{ 70-20 \texttt{i} }{ 0-10 \texttt{i} }$$

Evaluate

$$2+7i$$

Solution Steps

Multiply both numerator and denominator by imaginary unit i.

$$\frac{\left(70-20i\right)i}{-10i^{2}}$$

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

$$\frac{\left(70-20i\right)i}{10}$$

Multiply 70-20i times i.

$$\frac{70i-20i^{2}}{10}$$

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

$$\frac{70i-20\left(-1\right)}{10}$$

Do the multiplications in 70i-20\left(-1\right). Reorder the terms.

$$\frac{20+70i}{10}$$

Divide 20+70i by 10 to get 2+7i.

$$2+7i$$

Real Part

$$2$$

Solution Steps

Multiply both numerator and denominator of \frac{70-20i}{-10i} by imaginary unit i.

$$Re(\frac{\left(70-20i\right)i}{-10i^{2}})$$

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

$$Re(\frac{\left(70-20i\right)i}{10})$$

Multiply 70-20i times i.

$$Re(\frac{70i-20i^{2}}{10})$$

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

$$Re(\frac{70i-20\left(-1\right)}{10})$$

Do the multiplications in 70i-20\left(-1\right). Reorder the terms.

$$Re(\frac{20+70i}{10})$$

Divide 20+70i by 10 to get 2+7i.

$$Re(2+7i)$$

The real part of 2+7i is 2.

$$2$$