Solve -9+7i/-6i

$$\frac { - 9 + 7 i } { - 6 i }$$

Evaluate

$$-\frac{7}{6}-\frac{3}{2}i\approx -1.166666667-1.5i$$

Solution Steps

Multiply both numerator and denominator by imaginary unit i.

$$\frac{\left(-9+7i\right)i}{-6i^{2}}$$

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

$$\frac{\left(-9+7i\right)i}{6}$$

Multiply -9+7i times i.

$$\frac{-9i+7i^{2}}{6}$$

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

$$\frac{-9i+7\left(-1\right)}{6}$$

Do the multiplications in -9i+7\left(-1\right). Reorder the terms.

$$\frac{-7-9i}{6}$$

Divide -7-9i by 6 to get -\frac{7}{6}-\frac{3}{2}i.

$$-\frac{7}{6}-\frac{3}{2}i$$

Real Part

$$-\frac{7}{6} = -1\frac{1}{6} = -1.1666666666666667$$

Solution Steps

Multiply both numerator and denominator of \frac{-9+7i}{-6i} by imaginary unit i.

$$Re(\frac{\left(-9+7i\right)i}{-6i^{2}})$$

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

$$Re(\frac{\left(-9+7i\right)i}{6})$$

Multiply -9+7i times i.

$$Re(\frac{-9i+7i^{2}}{6})$$

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

$$Re(\frac{-9i+7\left(-1\right)}{6})$$

Do the multiplications in -9i+7\left(-1\right). Reorder the terms.

$$Re(\frac{-7-9i}{6})$$

Divide -7-9i by 6 to get -\frac{7}{6}-\frac{3}{2}i.

$$Re(-\frac{7}{6}-\frac{3}{2}i)$$

The real part of -\frac{7}{6}-\frac{3}{2}i is -\frac{7}{6}.

$$-\frac{7}{6}$$