Solve (i^14+i^11)(3i^11)

$$( i ^ { 14 } + i ^ { 11 } ) ( 3 i ^ { 11 } )$$

Evaluate

$$-3+3i$$

Solution Steps

Calculate i to the power of 14 and get -1.

$$\left(-1+i^{11}\right)\times 3i^{11}$$

Calculate i to the power of 11 and get -i.

$$\left(-1-i\right)\times 3i^{11}$$

Multiply -1-i and 3 to get -3-3i.

$$\left(-3-3i\right)i^{11}$$

Calculate i to the power of 11 and get -i.

$$\left(-3-3i\right)\left(-i\right)$$

Multiply -3-3i and -i to get -3+3i.

$$-3+3i$$

Real Part

$$-3$$

Solution Steps

Calculate i to the power of 14 and get -1.

$$Re(\left(-1+i^{11}\right)\times 3i^{11})$$

Calculate i to the power of 11 and get -i.

$$Re(\left(-1-i\right)\times 3i^{11})$$

Multiply -1-i and 3 to get -3-3i.

$$Re(\left(-3-3i\right)i^{11})$$

Calculate i to the power of 11 and get -i.

$$Re(\left(-3-3i\right)\left(-i\right))$$

Multiply -3-3i and -i to get -3+3i.

$$Re(-3+3i)$$

The real part of -3+3i is -3.

$$-3$$