Solve (6-4i)(6+4i)

$$( 6 - 4 i ) ( 6 + 4 i )$$

Evaluate

$$52$$

Solution Steps

Multiply complex numbers 6-4i and 6+4i like you multiply binomials.

$$6\times 6+6\times \left(4i\right)-4i\times 6-4\times 4i^{2}$$

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

$$6\times 6+6\times \left(4i\right)-4i\times 6-4\times 4\left(-1\right)$$

Do the multiplications.

$$36+24i-24i+16$$

Combine the real and imaginary parts.

$$36+16+\left(24-24\right)i$$

Do the additions.

$$52$$

Real Part

$$52$$

Solution Steps

Multiply complex numbers 6-4i and 6+4i like you multiply binomials.

$$Re(6\times 6+6\times \left(4i\right)-4i\times 6-4\times 4i^{2})$$

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

$$Re(6\times 6+6\times \left(4i\right)-4i\times 6-4\times 4\left(-1\right))$$

Do the multiplications in 6\times 6+6\times \left(4i\right)-4i\times 6-4\times 4\left(-1\right).

$$Re(36+24i-24i+16)$$

Combine the real and imaginary parts in 36+24i-24i+16.

$$Re(36+16+\left(24-24\right)i)$$

Do the additions in 36+16+\left(24-24\right)i.

$$Re(52)$$

The real part of 52 is 52.

$$52$$