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

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

Evaluate

$$-1-2i$$

Solution Steps

Multiply 3-4i and 1-2i to get -5-10i.

$$\frac{-5-10i}{1-4i^{2}}$$

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

$$\frac{-5-10i}{1-4\left(-1\right)}$$

Multiply 4 and -1 to get -4.

$$\frac{-5-10i}{1-\left(-4\right)}$$

The opposite of -4 is 4.

$$\frac{-5-10i}{1+4}$$

Add 1 and 4 to get 5.

$$\frac{-5-10i}{5}$$

Divide -5-10i by 5 to get -1-2i.

$$-1-2i$$

Real Part

$$-1$$

Solution Steps

Multiply 3-4i and 1-2i to get -5-10i.

$$Re(\frac{-5-10i}{1-4i^{2}})$$

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

$$Re(\frac{-5-10i}{1-4\left(-1\right)})$$

Multiply 4 and -1 to get -4.

$$Re(\frac{-5-10i}{1-\left(-4\right)})$$

The opposite of -4 is 4.

$$Re(\frac{-5-10i}{1+4})$$

Add 1 and 4 to get 5.

$$Re(\frac{-5-10i}{5})$$

Divide -5-10i by 5 to get -1-2i.

$$Re(-1-2i)$$

The real part of -1-2i is -1.

$$-1$$