Solve (1+3i)^2-(2i)^2/-3+4i

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

Evaluate

$$\frac{36}{25}-\frac{2}{25}i=1.44-0.08i$$

Solution Steps

Calculate 1+3i to the power of 2 and get -8+6i.

$$\frac{-8+6i-\left(2i\right)^{2}}{-3+4i}$$

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

$$\frac{-8+6i-\left(-4\right)}{-3+4i}$$

The opposite of -4 is 4.

$$\frac{-8+6i+4}{-3+4i}$$

Add -8+6i and 4 to get -4+6i.

$$\frac{-4+6i}{-3+4i}$$

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

$$\frac{\left(-4+6i\right)\left(-3-4i\right)}{\left(-3+4i\right)\left(-3-4i\right)}$$

Do the multiplications in \frac{\left(-4+6i\right)\left(-3-4i\right)}{\left(-3+4i\right)\left(-3-4i\right)}.

$$\frac{36-2i}{25}$$

Divide 36-2i by 25 to get \frac{36}{25}-\frac{2}{25}i.

$$\frac{36}{25}-\frac{2}{25}i$$

Real Part

$$\frac{36}{25} = 1\frac{11}{25} = 1.44$$

Solution Steps

Calculate 1+3i to the power of 2 and get -8+6i.

$$Re(\frac{-8+6i-\left(2i\right)^{2}}{-3+4i})$$

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

$$Re(\frac{-8+6i-\left(-4\right)}{-3+4i})$$

The opposite of -4 is 4.

$$Re(\frac{-8+6i+4}{-3+4i})$$

Add -8+6i and 4 to get -4+6i.

$$Re(\frac{-4+6i}{-3+4i})$$

Multiply both numerator and denominator of \frac{-4+6i}{-3+4i} by the complex conjugate of the denominator, -3-4i.

$$Re(\frac{\left(-4+6i\right)\left(-3-4i\right)}{\left(-3+4i\right)\left(-3-4i\right)})$$

Do the multiplications in \frac{\left(-4+6i\right)\left(-3-4i\right)}{\left(-3+4i\right)\left(-3-4i\right)}.

$$Re(\frac{36-2i}{25})$$

Divide 36-2i by 25 to get \frac{36}{25}-\frac{2}{25}i.

$$Re(\frac{36}{25}-\frac{2}{25}i)$$

The real part of \frac{36}{25}-\frac{2}{25}i is \frac{36}{25}.

$$\frac{36}{25}$$