Solve (-12+i)(-12-i)

$$( - 12 + i ) ( - 12 - i )$$

Evaluate

$$145$$

Solution Steps

Multiply complex numbers -12+i and -12-i like you multiply binomials.

$$-12\left(-12\right)-12\left(-i\right)-12i-i^{2}$$

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

$$-12\left(-12\right)-12\left(-i\right)-12i-\left(-1\right)$$

Do the multiplications.

$$144+12i-12i+1$$

Combine the real and imaginary parts.

$$144+1+\left(12-12\right)i$$

Do the additions.

$$145$$

Real Part

$$145$$

Solution Steps

Multiply complex numbers -12+i and -12-i like you multiply binomials.

$$Re(-12\left(-12\right)-12\left(-i\right)-12i-i^{2})$$

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

$$Re(-12\left(-12\right)-12\left(-i\right)-12i-\left(-1\right))$$

Do the multiplications in -12\left(-12\right)-12\left(-i\right)-12i-\left(-1\right).

$$Re(144+12i-12i+1)$$

Combine the real and imaginary parts in 144+12i-12i+1.

$$Re(144+1+\left(12-12\right)i)$$

Do the additions in 144+1+\left(12-12\right)i.

$$Re(145)$$

The real part of 145 is 145.

$$145$$