Solve (5/2-i)^2

$$( \frac { 5 } { 2 - i } ) ^ { 2 }$$

Evaluate

$$3+4i$$

Solution Steps

Multiply both numerator and denominator of \frac{5}{2-i} by the complex conjugate of the denominator, 2+i.

$$\left(\frac{5\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}\right)^{2}$$

Do the multiplications in \frac{5\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}.

$$\left(\frac{10+5i}{5}\right)^{2}$$

Divide 10+5i by 5 to get 2+i.

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

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

$$3+4i$$

Real Part

$$3$$

Solution Steps

Multiply both numerator and denominator of \frac{5}{2-i} by the complex conjugate of the denominator, 2+i.

$$Re(\left(\frac{5\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}\right)^{2})$$

Do the multiplications in \frac{5\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}.

$$Re(\left(\frac{10+5i}{5}\right)^{2})$$

Divide 10+5i by 5 to get 2+i.

$$Re(\left(2+i\right)^{2})$$

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

$$Re(3+4i)$$

The real part of 3+4i is 3.

$$3$$