Solve i^2+2/1+i

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

Evaluate

$$-i$$

Solution Steps

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

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

Multiply both numerator and denominator of \frac{2}{1+i} by the complex conjugate of the denominator, 1-i.

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

Do the multiplications in \frac{2\left(1-i\right)}{\left(1+i\right)\left(1-i\right)}.

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

Divide 2-2i by 2 to get 1-i.

$$-1+\left(1-i\right)$$

Add -1 and 1-i to get -i.

$$-i$$

Real Part

$$0$$

Solution Steps

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

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

Multiply both numerator and denominator of \frac{2}{1+i} by the complex conjugate of the denominator, 1-i.

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

Do the multiplications in \frac{2\left(1-i\right)}{\left(1+i\right)\left(1-i\right)}.

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

Divide 2-2i by 2 to get 1-i.

$$Re(-1+\left(1-i\right))$$

Add -1 and 1-i to get -i.

$$Re(-i)$$

The real part of -i is 0.

$$0$$