Solve (6+4i)(3-7i)

$$( 6 + 4 i ) ( 3 - 7 i )$$

Evaluate

$$46-30i$$

Solution Steps

Multiply complex numbers 6+4i and 3-7i like you multiply binomials.

$$6\times 3+6\times \left(-7i\right)+4i\times 3+4\left(-7\right)i^{2}$$

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

$$6\times 3+6\times \left(-7i\right)+4i\times 3+4\left(-7\right)\left(-1\right)$$

Do the multiplications.

$$18-42i+12i+28$$

Combine the real and imaginary parts.

$$18+28+\left(-42+12\right)i$$

Do the additions.

$$46-30i$$

Real Part

$$46$$

Solution Steps

Multiply complex numbers 6+4i and 3-7i like you multiply binomials.

$$Re(6\times 3+6\times \left(-7i\right)+4i\times 3+4\left(-7\right)i^{2})$$

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

$$Re(6\times 3+6\times \left(-7i\right)+4i\times 3+4\left(-7\right)\left(-1\right))$$

Do the multiplications in 6\times 3+6\times \left(-7i\right)+4i\times 3+4\left(-7\right)\left(-1\right).

$$Re(18-42i+12i+28)$$

Combine the real and imaginary parts in 18-42i+12i+28.

$$Re(18+28+\left(-42+12\right)i)$$

Do the additions in 18+28+\left(-42+12\right)i.

$$Re(46-30i)$$

The real part of 46-30i is 46.

$$46$$