Solve 24i^6-36i^16+48i^24/12i^8

$$\frac { 24 i ^ { 6 } - 36 i ^ { 16 } + 48 i ^ { 24 } } { 12 i ^ { 8 } }$$

Evaluate

$$-1$$

Solution Steps

Calculate i to the power of 6 and get -1.

$$\frac{24\left(-1\right)-36i^{16}+48i^{24}}{12i^{8}}$$

Multiply 24 and -1 to get -24.

$$\frac{-24-36i^{16}+48i^{24}}{12i^{8}}$$

Calculate i to the power of 16 and get 1.

$$\frac{-24-36\times 1+48i^{24}}{12i^{8}}$$

Multiply 36 and 1 to get 36.

$$\frac{-24-36+48i^{24}}{12i^{8}}$$

Subtract 36 from -24 to get -60.

$$\frac{-60+48i^{24}}{12i^{8}}$$

Calculate i to the power of 24 and get 1.

$$\frac{-60+48\times 1}{12i^{8}}$$

Multiply 48 and 1 to get 48.

$$\frac{-60+48}{12i^{8}}$$

Add -60 and 48 to get -12.

$$\frac{-12}{12i^{8}}$$

Calculate i to the power of 8 and get 1.

$$\frac{-12}{12\times 1}$$

Multiply 12 and 1 to get 12.

$$\frac{-12}{12}$$

Divide -12 by 12 to get -1.

$$-1$$

Real Part

$$-1$$

Solution Steps

Calculate i to the power of 6 and get -1.

$$Re(\frac{24\left(-1\right)-36i^{16}+48i^{24}}{12i^{8}})$$

Multiply 24 and -1 to get -24.

$$Re(\frac{-24-36i^{16}+48i^{24}}{12i^{8}})$$

Calculate i to the power of 16 and get 1.

$$Re(\frac{-24-36\times 1+48i^{24}}{12i^{8}})$$

Multiply 36 and 1 to get 36.

$$Re(\frac{-24-36+48i^{24}}{12i^{8}})$$

Subtract 36 from -24 to get -60.

$$Re(\frac{-60+48i^{24}}{12i^{8}})$$

Calculate i to the power of 24 and get 1.

$$Re(\frac{-60+48\times 1}{12i^{8}})$$

Multiply 48 and 1 to get 48.

$$Re(\frac{-60+48}{12i^{8}})$$

Add -60 and 48 to get -12.

$$Re(\frac{-12}{12i^{8}})$$

Calculate i to the power of 8 and get 1.

$$Re(\frac{-12}{12\times 1})$$

Multiply 12 and 1 to get 12.

$$Re(\frac{-12}{12})$$

Divide -12 by 12 to get -1.

$$Re(-1)$$

The real part of -1 is -1.

$$-1$$