Solve (8+5i)(6+3i)=

$$( 8 + 5 i ) ( 6 + 3 i ) =$$

Evaluate

$$33+54i$$

Solution Steps

Multiply complex numbers 8+5i and 6+3i like you multiply binomials.

$$8\times 6+8\times \left(3i\right)+5i\times 6+5\times 3i^{2}$$

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

$$8\times 6+8\times \left(3i\right)+5i\times 6+5\times 3\left(-1\right)$$

Do the multiplications.

$$48+24i+30i-15$$

Combine the real and imaginary parts.

$$48-15+\left(24+30\right)i$$

Do the additions.

$$33+54i$$

Real Part

$$33$$

Solution Steps

Multiply complex numbers 8+5i and 6+3i like you multiply binomials.

$$Re(8\times 6+8\times \left(3i\right)+5i\times 6+5\times 3i^{2})$$

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

$$Re(8\times 6+8\times \left(3i\right)+5i\times 6+5\times 3\left(-1\right))$$

Do the multiplications in 8\times 6+8\times \left(3i\right)+5i\times 6+5\times 3\left(-1\right).

$$Re(48+24i+30i-15)$$

Combine the real and imaginary parts in 48+24i+30i-15.

$$Re(48-15+\left(24+30\right)i)$$

Do the additions in 48-15+\left(24+30\right)i.

$$Re(33+54i)$$

The real part of 33+54i is 33.

$$33$$