Solve (5+4i)*(6+3i)

$$( 5 + 4 i ) \times ( 6 + 3 i )$$

Evaluate

$$18+39i$$

Solution Steps

Multiply complex numbers 5+4i and 6+3i like you multiply binomials.

$$5\times 6+5\times \left(3i\right)+4i\times 6+4\times 3i^{2}$$

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

$$5\times 6+5\times \left(3i\right)+4i\times 6+4\times 3\left(-1\right)$$

Do the multiplications.

$$30+15i+24i-12$$

Combine the real and imaginary parts.

$$30-12+\left(15+24\right)i$$

Do the additions.

$$18+39i$$

Real Part

$$18$$

Solution Steps

Multiply complex numbers 5+4i and 6+3i like you multiply binomials.

$$Re(5\times 6+5\times \left(3i\right)+4i\times 6+4\times 3i^{2})$$

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

$$Re(5\times 6+5\times \left(3i\right)+4i\times 6+4\times 3\left(-1\right))$$

Do the multiplications in 5\times 6+5\times \left(3i\right)+4i\times 6+4\times 3\left(-1\right).

$$Re(30+15i+24i-12)$$

Combine the real and imaginary parts in 30+15i+24i-12.

$$Re(30-12+\left(15+24\right)i)$$

Do the additions in 30-12+\left(15+24\right)i.

$$Re(18+39i)$$

The real part of 18+39i is 18.

$$18$$