Solve 6+5i/-2i

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

Evaluate

$$-\frac{5}{2}+3i=-2.5+3i$$

Solution Steps

Multiply both numerator and denominator by imaginary unit i.

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

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

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

Multiply 6+5i times i.

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

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

$$\frac{6i+5\left(-1\right)}{2}$$

Do the multiplications in 6i+5\left(-1\right). Reorder the terms.

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

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

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

Real Part

$$-\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Solution Steps

Multiply both numerator and denominator of \frac{6+5i}{-2i} by imaginary unit i.

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

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

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

Multiply 6+5i times i.

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

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

$$Re(\frac{6i+5\left(-1\right)}{2})$$

Do the multiplications in 6i+5\left(-1\right). Reorder the terms.

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

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

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

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

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