Solve (2-5i)^2/1-4i

$$\frac { ( 2 - 5 i ) ^ { 2 } } { 1 - 4 i }$$

Evaluate

$$\frac{59}{17}-\frac{104}{17}i\approx 3.470588235-6.117647059i$$

Solution Steps

Calculate 2-5i to the power of 2 and get -21-20i.

$$\frac{-21-20i}{1-4i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, 1+4i.

$$\frac{\left(-21-20i\right)\left(1+4i\right)}{\left(1-4i\right)\left(1+4i\right)}$$

Do the multiplications in \frac{\left(-21-20i\right)\left(1+4i\right)}{\left(1-4i\right)\left(1+4i\right)}.

$$\frac{59-104i}{17}$$

Divide 59-104i by 17 to get \frac{59}{17}-\frac{104}{17}i.

$$\frac{59}{17}-\frac{104}{17}i$$

Real Part

$$\frac{59}{17} = 3\frac{8}{17} = 3.4705882352941178$$

Solution Steps

Calculate 2-5i to the power of 2 and get -21-20i.

$$Re(\frac{-21-20i}{1-4i})$$

Multiply both numerator and denominator of \frac{-21-20i}{1-4i} by the complex conjugate of the denominator, 1+4i.

$$Re(\frac{\left(-21-20i\right)\left(1+4i\right)}{\left(1-4i\right)\left(1+4i\right)})$$

Do the multiplications in \frac{\left(-21-20i\right)\left(1+4i\right)}{\left(1-4i\right)\left(1+4i\right)}.

$$Re(\frac{59-104i}{17})$$

Divide 59-104i by 17 to get \frac{59}{17}-\frac{104}{17}i.

$$Re(\frac{59}{17}-\frac{104}{17}i)$$

The real part of \frac{59}{17}-\frac{104}{17}i is \frac{59}{17}.

$$\frac{59}{17}$$