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

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

Evaluate

$$i$$

Solution Steps

Cancel out 1+i in both numerator and denominator.

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

Multiply both numerator and denominator by the complex conjugate of the denominator, 1+i.

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

Do the multiplications in \frac{\left(1+i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}.

$$\frac{2i}{2}$$

Divide 2i by 2 to get i.

$$i$$

Real Part

$$0$$

Solution Steps

Cancel out 1+i in both numerator and denominator.

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

Multiply both numerator and denominator of \frac{1+i}{1-i} by the complex conjugate of the denominator, 1+i.

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

Do the multiplications in \frac{\left(1+i\right)\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}.

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

Divide 2i by 2 to get i.

$$Re(i)$$

The real part of i is 0.

$$0$$