Solve 4i^23+1/2i^15=

$$4 i ^ { 23 } + \frac { 1 } { 2 } i ^ { 15 } =$$

Evaluate

$$-\frac{9}{2}i=-4.5i$$

Solution Steps

Calculate i to the power of 23 and get -i.

$$4\left(-i\right)+\frac{1}{2}i^{15}$$

Multiply 4 and -i to get -4i.

$$-4i+\frac{1}{2}i^{15}$$

Calculate i to the power of 15 and get -i.

$$-4i+\frac{1}{2}\left(-i\right)$$

Multiply \frac{1}{2} and -i to get -\frac{1}{2}i.

$$-4i-\frac{1}{2}i$$

Subtract \frac{1}{2}i from -4i to get -\frac{9}{2}i.

$$-\frac{9}{2}i$$

Real Part

$$0$$

Solution Steps

Calculate i to the power of 23 and get -i.

$$Re(4\left(-i\right)+\frac{1}{2}i^{15})$$

Multiply 4 and -i to get -4i.

$$Re(-4i+\frac{1}{2}i^{15})$$

Calculate i to the power of 15 and get -i.

$$Re(-4i+\frac{1}{2}\left(-i\right))$$

Multiply \frac{1}{2} and -i to get -\frac{1}{2}i.

$$Re(-4i-\frac{1}{2}i)$$

Subtract \frac{1}{2}i from -4i to get -\frac{9}{2}i.

$$Re(-\frac{9}{2}i)$$

The real part of -\frac{9}{2}i is 0.

$$0$$