Solve -4+5i/6i

$$\frac { - 4 + 5 i } { 6 i }$$

Evaluate

$$\frac{5}{6}+\frac{2}{3}i\approx 0.833333333+0.666666667i$$

Solution Steps

Multiply both numerator and denominator by imaginary unit i.

$$\frac{\left(-4+5i\right)i}{6i^{2}}$$

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

$$\frac{\left(-4+5i\right)i}{-6}$$

Multiply -4+5i times i.

$$\frac{-4i+5i^{2}}{-6}$$

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

$$\frac{-4i+5\left(-1\right)}{-6}$$

Do the multiplications in -4i+5\left(-1\right). Reorder the terms.

$$\frac{-5-4i}{-6}$$

Divide -5-4i by -6 to get \frac{5}{6}+\frac{2}{3}i.

$$\frac{5}{6}+\frac{2}{3}i$$

Real Part

$$\frac{5}{6} = 0.8333333333333334$$

Solution Steps

Multiply both numerator and denominator of \frac{-4+5i}{6i} by imaginary unit i.

$$Re(\frac{\left(-4+5i\right)i}{6i^{2}})$$

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

$$Re(\frac{\left(-4+5i\right)i}{-6})$$

Multiply -4+5i times i.

$$Re(\frac{-4i+5i^{2}}{-6})$$

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

$$Re(\frac{-4i+5\left(-1\right)}{-6})$$

Do the multiplications in -4i+5\left(-1\right). Reorder the terms.

$$Re(\frac{-5-4i}{-6})$$

Divide -5-4i by -6 to get \frac{5}{6}+\frac{2}{3}i.

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

The real part of \frac{5}{6}+\frac{2}{3}i is \frac{5}{6}.

$$\frac{5}{6}$$