Solve 2+5i/3i

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

Evaluate

$$\frac{5}{3}-\frac{2}{3}i\approx 1.666666667-0.666666667i$$

Solution Steps

Multiply both numerator and denominator by imaginary unit i.

$$\frac{\left(2+5i\right)i}{3i^{2}}$$

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

$$\frac{\left(2+5i\right)i}{-3}$$

Multiply 2+5i times i.

$$\frac{2i+5i^{2}}{-3}$$

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

$$\frac{2i+5\left(-1\right)}{-3}$$

Do the multiplications in 2i+5\left(-1\right). Reorder the terms.

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

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

$$\frac{5}{3}-\frac{2}{3}i$$

Real Part

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$

Solution Steps

Multiply both numerator and denominator of \frac{2+5i}{3i} by imaginary unit i.

$$Re(\frac{\left(2+5i\right)i}{3i^{2}})$$

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

$$Re(\frac{\left(2+5i\right)i}{-3})$$

Multiply 2+5i times i.

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

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

$$Re(\frac{2i+5\left(-1\right)}{-3})$$

Do the multiplications in 2i+5\left(-1\right). Reorder the terms.

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

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

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

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

$$\frac{5}{3}$$