Solve (123-i)(212+i)=

$$( 123 - i ) ( 212 + i ) =$$

Evaluate

$$26077-89i$$

Solution Steps

Multiply complex numbers 123-i and 212+i like you multiply binomials.

$$123\times 212+123i-i\times 212-i^{2}$$

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

$$123\times 212+123i-i\times 212-\left(-1\right)$$

Do the multiplications.

$$26076+123i-212i+1$$

Combine the real and imaginary parts.

$$26076+1+\left(123-212\right)i$$

Do the additions.

$$26077-89i$$

Real Part

$$26077$$

Solution Steps

Multiply complex numbers 123-i and 212+i like you multiply binomials.

$$Re(123\times 212+123i-i\times 212-i^{2})$$

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

$$Re(123\times 212+123i-i\times 212-\left(-1\right))$$

Do the multiplications in 123\times 212+123i-i\times 212-\left(-1\right).

$$Re(26076+123i-212i+1)$$

Combine the real and imaginary parts in 26076+123i-212i+1.

$$Re(26076+1+\left(123-212\right)i)$$

Do the additions in 26076+1+\left(123-212\right)i.

$$Re(26077-89i)$$

The real part of 26077-89i is 26077.

$$26077$$