Solve -3-7i/-1+2i*1-2i/1-2i

$$\frac { - 3 - 7 i } { - 1 + 2 i } \cdot \frac { 1 - 2 i } { 1 - 2 i }$$

Evaluate

$$-\frac{11}{5}+\frac{13}{5}i=-2.2+2.6i$$

Solution Steps

Divide 1-2i by 1-2i to get 1.

$$\frac{-3-7i}{-1+2i}\times 1$$

Multiply both numerator and denominator of \frac{-3-7i}{-1+2i} by the complex conjugate of the denominator, -1-2i.

$$\frac{\left(-3-7i\right)\left(-1-2i\right)}{\left(-1+2i\right)\left(-1-2i\right)}\times 1$$

Do the multiplications in \frac{\left(-3-7i\right)\left(-1-2i\right)}{\left(-1+2i\right)\left(-1-2i\right)}.

$$\frac{-11+13i}{5}\times 1$$

Divide -11+13i by 5 to get -\frac{11}{5}+\frac{13}{5}i.

$$\left(-\frac{11}{5}+\frac{13}{5}i\right)\times 1$$

Multiply -\frac{11}{5}+\frac{13}{5}i and 1 to get -\frac{11}{5}+\frac{13}{5}i.

$$-\frac{11}{5}+\frac{13}{5}i$$

Real Part

$$-\frac{11}{5} = -2\frac{1}{5} = -2.2$$

Solution Steps

Divide 1-2i by 1-2i to get 1.

$$Re(\frac{-3-7i}{-1+2i}\times 1)$$

Multiply both numerator and denominator of \frac{-3-7i}{-1+2i} by the complex conjugate of the denominator, -1-2i.

$$Re(\frac{\left(-3-7i\right)\left(-1-2i\right)}{\left(-1+2i\right)\left(-1-2i\right)}\times 1)$$

Do the multiplications in \frac{\left(-3-7i\right)\left(-1-2i\right)}{\left(-1+2i\right)\left(-1-2i\right)}.

$$Re(\frac{-11+13i}{5}\times 1)$$

Divide -11+13i by 5 to get -\frac{11}{5}+\frac{13}{5}i.

$$Re(\left(-\frac{11}{5}+\frac{13}{5}i\right)\times 1)$$

Multiply -\frac{11}{5}+\frac{13}{5}i and 1 to get -\frac{11}{5}+\frac{13}{5}i.

$$Re(-\frac{11}{5}+\frac{13}{5}i)$$

The real part of -\frac{11}{5}+\frac{13}{5}i is -\frac{11}{5}.

$$-\frac{11}{5}$$