Solve 1/(2-i)^2

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

Evaluate

$$\frac{3}{25}+\frac{4}{25}i=0.12+0.16i$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

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

To raise a power to another power, multiply the exponents.

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

Multiply 2 times -1.

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

Raise 2-i to the power -2.

$$\frac{3}{25}+\frac{4}{25}i$$

Real Part

$$\frac{3}{25} = 0.12$$

Solution Steps

Calculate 2-i to the power of 2 and get 3-4i.

$$Re(\frac{1}{3-4i})$$

Multiply both numerator and denominator of \frac{1}{3-4i} by the complex conjugate of the denominator, 3+4i.

$$Re(\frac{1\left(3+4i\right)}{\left(3-4i\right)\left(3+4i\right)})$$

Do the multiplications in \frac{1\left(3+4i\right)}{\left(3-4i\right)\left(3+4i\right)}.

$$Re(\frac{3+4i}{25})$$

Divide 3+4i by 25 to get \frac{3}{25}+\frac{4}{25}i.

$$Re(\frac{3}{25}+\frac{4}{25}i)$$

The real part of \frac{3}{25}+\frac{4}{25}i is \frac{3}{25}.

$$\frac{3}{25}$$