Solve 1/4:(1+2i)^2

$$\frac { 1 } { 4 } : ( 1 + 2 i ) ^ { 2 }$$

Evaluate

$$-\frac{3}{100}-\frac{1}{25}i=-0.03-0.04i$$

Solution Steps

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

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

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

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

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

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

Divide -\frac{3}{4}-i by 25 to get -\frac{3}{100}-\frac{1}{25}i.

$$-\frac{3}{100}-\frac{1}{25}i$$

Real Part

$$-\frac{3}{100} = -0.03$$

Solution Steps

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

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

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

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

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

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

Divide -\frac{3}{4}-i by 25 to get -\frac{3}{100}-\frac{1}{25}i.

$$Re(-\frac{3}{100}-\frac{1}{25}i)$$

The real part of -\frac{3}{100}-\frac{1}{25}i is -\frac{3}{100}.

$$-\frac{3}{100}$$