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

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

Evaluate

$$-1+i$$

Solution Steps

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

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

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

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

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

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

Multiply 1 and -1+i to get -1+i.

$$-1+i$$

Real Part

$$-1$$

Solution Steps

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

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

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

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

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

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

Multiply 1 and -1+i to get -1+i.

$$Re(-1+i)$$

The real part of -1+i is -1.

$$-1$$