Solve -1/3i^89i^19

$$- \frac{ 1 }{ 3 } { i }^{ 8 } 9 { i }^{ 19 }$$

Evaluate

$$3i$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 19 to get 27.

$$-\frac{1}{3}i^{27}\times 9$$

Calculate i to the power of 27 and get -i.

$$-\frac{1}{3}\left(-i\right)\times 9$$

Multiply -\frac{1}{3} and -i to get \frac{1}{3}i.

$$\frac{1}{3}i\times 9$$

Multiply \frac{1}{3}i and 9 to get 3i.

$$3i$$

Real Part

$$0$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 19 to get 27.

$$Re(-\frac{1}{3}i^{27}\times 9)$$

Calculate i to the power of 27 and get -i.

$$Re(-\frac{1}{3}\left(-i\right)\times 9)$$

Multiply -\frac{1}{3} and -i to get \frac{1}{3}i.

$$Re(\frac{1}{3}i\times 9)$$

Multiply \frac{1}{3}i and 9 to get 3i.

$$Re(3i)$$

The real part of 3i is 0.

$$0$$