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

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

Evaluate

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

Solution Steps

Calculate i to the power of 5 and get i.

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

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

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

Multiply both numerator and denominator of \frac{1+i}{-2i} by imaginary unit i.

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

Divide -1+i by 2 to get -\frac{1}{2}+\frac{1}{2}i.

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

Add i and \frac{1}{2}-\frac{1}{2}i to 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 5 and get i.

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

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

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

Multiply both numerator and denominator of \frac{1+i}{-2i} by imaginary unit i.

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

Divide -1+i by 2 to get -\frac{1}{2}+\frac{1}{2}i.

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

Add i and \frac{1}{2}-\frac{1}{2}i to 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}.

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