Solve (2+i)^2/(3-4i)(2+i)

$$\frac { ( 2 + i ) ^ { 2 } } { ( 3 - 4 i ) ( 2 + i ) }$$

Evaluate

$$\frac{2}{25}+\frac{11}{25}i=0.08+0.44i$$

Solution Steps

Cancel out 2+i in both numerator and denominator.

$$\frac{2+i}{3-4i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, 3+4i.

$$\frac{\left(2+i\right)\left(3+4i\right)}{\left(3-4i\right)\left(3+4i\right)}$$

Do the multiplications in \frac{\left(2+i\right)\left(3+4i\right)}{\left(3-4i\right)\left(3+4i\right)}.

$$\frac{2+11i}{25}$$

Divide 2+11i by 25 to get \frac{2}{25}+\frac{11}{25}i.

$$\frac{2}{25}+\frac{11}{25}i$$

Real Part

$$\frac{2}{25} = 0.08$$

Solution Steps

Cancel out 2+i in both numerator and denominator.

$$Re(\frac{2+i}{3-4i})$$

Multiply both numerator and denominator of \frac{2+i}{3-4i} by the complex conjugate of the denominator, 3+4i.

$$Re(\frac{\left(2+i\right)\left(3+4i\right)}{\left(3-4i\right)\left(3+4i\right)})$$

Do the multiplications in \frac{\left(2+i\right)\left(3+4i\right)}{\left(3-4i\right)\left(3+4i\right)}.

$$Re(\frac{2+11i}{25})$$

Divide 2+11i by 25 to get \frac{2}{25}+\frac{11}{25}i.

$$Re(\frac{2}{25}+\frac{11}{25}i)$$

The real part of \frac{2}{25}+\frac{11}{25}i is \frac{2}{25}.

$$\frac{2}{25}$$