Solve (-14+0.5i)(-14-0.5i)

$$( - 14 + 0.5 i ) ( - 14 - 0.5 i )$$

Evaluate

$$196.25$$

Solution Steps

Multiply complex numbers -14+0.5i and -14-0.5i like you multiply binomials.

$$-14\left(-14\right)-14\times \left(-0.5i\right)+0.5i\left(-14\right)+0.5\left(-0.5\right)i^{2}$$

By definition, i^{2} is -1.

$$-14\left(-14\right)-14\times \left(-0.5i\right)+0.5i\left(-14\right)+0.5\left(-0.5\right)\left(-1\right)$$

Do the multiplications.

$$196+7i-7i+0.25$$

Combine the real and imaginary parts.

$$196+0.25+\left(7-7\right)i$$

Do the additions.

$$196.25$$

Real Part

$$196.25$$

Solution Steps

Multiply complex numbers -14+0.5i and -14-0.5i like you multiply binomials.

$$Re(-14\left(-14\right)-14\times \left(-0.5i\right)+0.5i\left(-14\right)+0.5\left(-0.5\right)i^{2})$$

By definition, i^{2} is -1.

$$Re(-14\left(-14\right)-14\times \left(-0.5i\right)+0.5i\left(-14\right)+0.5\left(-0.5\right)\left(-1\right))$$

Do the multiplications in -14\left(-14\right)-14\times \left(-0.5i\right)+0.5i\left(-14\right)+0.5\left(-0.5\right)\left(-1\right).

$$Re(196+7i-7i+0.25)$$

Combine the real and imaginary parts in 196+7i-7i+0.25.

$$Re(196+0.25+\left(7-7\right)i)$$

Do the additions in 196+0.25+\left(7-7\right)i.

$$Re(196.25)$$

The real part of 196.25 is 196.25.

$$196.25$$