Solve (1-i^-1)^-1

$$( 1 - i ^ { - 1 } ) ^ { - 1 }$$

Evaluate

$$\frac{1}{2}-\frac{1}{2}i=0.5-0.5i$$

Solution Steps

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

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

The opposite of -i is i.

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

Calculate 1+i to the power of -1 and get \frac{1}{2}-\frac{1}{2}i.

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

Real Part

$$\frac{1}{2} = 0.5$$

Solution Steps

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

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

The opposite of -i is i.

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

Calculate 1+i to the power of -1 and get \frac{1}{2}-\frac{1}{2}i.

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

The real part of \frac{1}{2}-\frac{1}{2}i is \frac{1}{2}.

$$\frac{1}{2}$$