Solve (1+i)^2/2-3i

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

Evaluate

$$-\frac{6}{13}+\frac{4}{13}i\approx -0.461538462+0.307692308i$$

Solution Steps

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

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

Multiply both numerator and denominator by the complex conjugate of the denominator, 2+3i.

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

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

$$\frac{-6+4i}{13}$$

Divide -6+4i by 13 to get -\frac{6}{13}+\frac{4}{13}i.

$$-\frac{6}{13}+\frac{4}{13}i$$

Real Part

$$-\frac{6}{13} = -0.46153846153846156$$

Solution Steps

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

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

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

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

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

$$Re(\frac{-6+4i}{13})$$

Divide -6+4i by 13 to get -\frac{6}{13}+\frac{4}{13}i.

$$Re(-\frac{6}{13}+\frac{4}{13}i)$$

The real part of -\frac{6}{13}+\frac{4}{13}i is -\frac{6}{13}.

$$-\frac{6}{13}$$