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

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

Evaluate

$$2i$$

Solution Steps

Do the additions in 1-1+2i.

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

Do the additions in 1-1-2i.

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

The opposite of -2i is 2i.

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

Add 2i and 2i to get 4i.

$$\frac{4i}{1-i^{2}}$$

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

$$\frac{4i}{1-\left(-1\right)}$$

The opposite of -1 is 1.

$$\frac{4i}{1+1}$$

Add 1 and 1 to get 2.

$$\frac{4i}{2}$$

Divide 4i by 2 to get 2i.

$$2i$$

Real Part

$$0$$

Solution Steps

Do the additions in 1-1+2i.

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

Do the additions in 1-1-2i.

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

The opposite of -2i is 2i.

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

Add 2i and 2i to get 4i.

$$Re(\frac{4i}{1-i^{2}})$$

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

$$Re(\frac{4i}{1-\left(-1\right)})$$

The opposite of -1 is 1.

$$Re(\frac{4i}{1+1})$$

Add 1 and 1 to get 2.

$$Re(\frac{4i}{2})$$

Divide 4i by 2 to get 2i.

$$Re(2i)$$

The real part of 2i is 0.

$$0$$