Solve (3-i+6i-2i^2)/3-2i

$$\frac { ( 3 - i + 6 i - 2 i ^ { 2 } ) } { 3 - 2 i }$$

Evaluate

$$\frac{5}{13}+\frac{25}{13}i\approx 0.384615385+1.923076923i$$

Solution Steps

Add 3-i and 6i to get 3+5i.

$$\frac{3+5i-2i^{2}}{3-2i}$$

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

$$\frac{3+5i-2\left(-1\right)}{3-2i}$$

Multiply 2 and -1 to get -2.

$$\frac{3+5i-\left(-2\right)}{3-2i}$$

The opposite of -2 is 2.

$$\frac{3+5i+2}{3-2i}$$

Add 3+5i and 2 to get 5+5i.

$$\frac{5+5i}{3-2i}$$

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

$$\frac{\left(5+5i\right)\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)}$$

Do the multiplications in \frac{\left(5+5i\right)\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)}.

$$\frac{5+25i}{13}$$

Divide 5+25i by 13 to get \frac{5}{13}+\frac{25}{13}i.

$$\frac{5}{13}+\frac{25}{13}i$$

Real Part

$$\frac{5}{13} = 0.38461538461538464$$

Solution Steps

Add 3-i and 6i to get 3+5i.

$$Re(\frac{3+5i-2i^{2}}{3-2i})$$

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

$$Re(\frac{3+5i-2\left(-1\right)}{3-2i})$$

Multiply 2 and -1 to get -2.

$$Re(\frac{3+5i-\left(-2\right)}{3-2i})$$

The opposite of -2 is 2.

$$Re(\frac{3+5i+2}{3-2i})$$

Add 3+5i and 2 to get 5+5i.

$$Re(\frac{5+5i}{3-2i})$$

Multiply both numerator and denominator of \frac{5+5i}{3-2i} by the complex conjugate of the denominator, 3+2i.

$$Re(\frac{\left(5+5i\right)\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)})$$

Do the multiplications in \frac{\left(5+5i\right)\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)}.

$$Re(\frac{5+25i}{13})$$

Divide 5+25i by 13 to get \frac{5}{13}+\frac{25}{13}i.

$$Re(\frac{5}{13}+\frac{25}{13}i)$$

The real part of \frac{5}{13}+\frac{25}{13}i is \frac{5}{13}.

$$\frac{5}{13}$$