Solve (-6+i)(-6-i)

$$( - 6 + i ) ( - 6 - i )$$

Evaluate

$$37$$

Solution Steps

Multiply complex numbers -6+i and -6-i like you multiply binomials.

$$-6\left(-6\right)-6\left(-i\right)-6i-i^{2}$$

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

$$-6\left(-6\right)-6\left(-i\right)-6i-\left(-1\right)$$

Do the multiplications.

$$36+6i-6i+1$$

Combine the real and imaginary parts.

$$36+1+\left(6-6\right)i$$

Do the additions.

$$37$$

Real Part

$$37$$

Solution Steps

Multiply complex numbers -6+i and -6-i like you multiply binomials.

$$Re(-6\left(-6\right)-6\left(-i\right)-6i-i^{2})$$

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

$$Re(-6\left(-6\right)-6\left(-i\right)-6i-\left(-1\right))$$

Do the multiplications in -6\left(-6\right)-6\left(-i\right)-6i-\left(-1\right).

$$Re(36+6i-6i+1)$$

Combine the real and imaginary parts in 36+6i-6i+1.

$$Re(36+1+\left(6-6\right)i)$$

Do the additions in 36+1+\left(6-6\right)i.

$$Re(37)$$

The real part of 37 is 37.

$$37$$