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

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

Evaluate

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

Solution Steps

Calculate 1+2i to the power of 2 and get -3+4i.

$$\frac{1-2i}{-3+4i}$$

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

$$\frac{\left(1-2i\right)\left(-3-4i\right)}{\left(-3+4i\right)\left(-3-4i\right)}$$

Do the multiplications in \frac{\left(1-2i\right)\left(-3-4i\right)}{\left(-3+4i\right)\left(-3-4i\right)}.

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

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

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

Real Part

$$-\frac{11}{25} = -0.44$$

Solution Steps

Calculate 1+2i to the power of 2 and get -3+4i.

$$Re(\frac{1-2i}{-3+4i})$$

Multiply both numerator and denominator of \frac{1-2i}{-3+4i} by the complex conjugate of the denominator, -3-4i.

$$Re(\frac{\left(1-2i\right)\left(-3-4i\right)}{\left(-3+4i\right)\left(-3-4i\right)})$$

Do the multiplications in \frac{\left(1-2i\right)\left(-3-4i\right)}{\left(-3+4i\right)\left(-3-4i\right)}.

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

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

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

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

$$-\frac{11}{25}$$