Solve 4-i/6i

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

Evaluate

$$-\frac{1}{6}-\frac{2}{3}i\approx -0.166666667-0.666666667i$$

Solution Steps

Multiply both numerator and denominator by imaginary unit i.

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

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

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

Multiply 4-i times i.

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

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

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

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

$$\frac{1+4i}{-6}$$

Divide 1+4i by -6 to get -\frac{1}{6}-\frac{2}{3}i.

$$-\frac{1}{6}-\frac{2}{3}i$$

Real Part

$$-\frac{1}{6} = -0.16666666666666666$$

Solution Steps

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

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

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

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

Multiply 4-i times i.

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

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

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

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

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

Divide 1+4i by -6 to get -\frac{1}{6}-\frac{2}{3}i.

$$Re(-\frac{1}{6}-\frac{2}{3}i)$$

The real part of -\frac{1}{6}-\frac{2}{3}i is -\frac{1}{6}.

$$-\frac{1}{6}$$