Solve i^-7(1/i^5)^-2

$$i ^ { - 7 } ( \frac { 1 } { i ^ { 5 } } ) ^ { - 2 }$$

Evaluate

$$-i$$

Solution Steps

Calculate i to the power of -7 and get i.

$$i\times \left(\frac{1}{i^{5}}\right)^{-2}$$

Calculate i to the power of 5 and get i.

$$i\times \left(\frac{1}{i}\right)^{-2}$$

Multiply both numerator and denominator of \frac{1}{i} by imaginary unit i.

$$i\times \left(\frac{i}{-1}\right)^{-2}$$

Divide i by -1 to get -i.

$$i\left(-i\right)^{-2}$$

Calculate -i to the power of -2 and get -1.

$$-i$$

Real Part

$$0$$

Solution Steps

Calculate i to the power of -7 and get i.

$$Re(i\times \left(\frac{1}{i^{5}}\right)^{-2})$$

Calculate i to the power of 5 and get i.

$$Re(i\times \left(\frac{1}{i}\right)^{-2})$$

Multiply both numerator and denominator of \frac{1}{i} by imaginary unit i.

$$Re(i\times \left(\frac{i}{-1}\right)^{-2})$$

Divide i by -1 to get -i.

$$Re(i\left(-i\right)^{-2})$$

Calculate -i to the power of -2 and get -1.

$$Re(-i)$$

The real part of -i is 0.

$$0$$