Solve (8+2i)(6+i)

$$( 8 + 2 i ) ( 6 + i )$$

Evaluate

$$46+20i$$

Solution Steps

Multiply complex numbers 8+2i and 6+i like you multiply binomials.

$$8\times 6+8i+2i\times 6+2i^{2}$$

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

$$8\times 6+8i+2i\times 6+2\left(-1\right)$$

Do the multiplications.

$$48+8i+12i-2$$

Combine the real and imaginary parts.

$$48-2+\left(8+12\right)i$$

Do the additions.

$$46+20i$$

Real Part

$$46$$

Solution Steps

Multiply complex numbers 8+2i and 6+i like you multiply binomials.

$$Re(8\times 6+8i+2i\times 6+2i^{2})$$

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

$$Re(8\times 6+8i+2i\times 6+2\left(-1\right))$$

Do the multiplications in 8\times 6+8i+2i\times 6+2\left(-1\right).

$$Re(48+8i+12i-2)$$

Combine the real and imaginary parts in 48+8i+12i-2.

$$Re(48-2+\left(8+12\right)i)$$

Do the additions in 48-2+\left(8+12\right)i.

$$Re(46+20i)$$

The real part of 46+20i is 46.

$$46$$