Solve (2+i)(6+5i)

$$( 2 + i ) ( 6 + 5 i )$$

Evaluate

$$7+16i$$

Solution Steps

Multiply complex numbers 2+i and 6+5i like you multiply binomials.

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

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

$$2\times 6+2\times \left(5i\right)+6i+5\left(-1\right)$$

Do the multiplications.

$$12+10i+6i-5$$

Combine the real and imaginary parts.

$$12-5+\left(10+6\right)i$$

Do the additions.

$$7+16i$$

Real Part

$$7$$

Solution Steps

Multiply complex numbers 2+i and 6+5i like you multiply binomials.

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

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

$$Re(2\times 6+2\times \left(5i\right)+6i+5\left(-1\right))$$

Do the multiplications in 2\times 6+2\times \left(5i\right)+6i+5\left(-1\right).

$$Re(12+10i+6i-5)$$

Combine the real and imaginary parts in 12+10i+6i-5.

$$Re(12-5+\left(10+6\right)i)$$

Do the additions in 12-5+\left(10+6\right)i.

$$Re(7+16i)$$

The real part of 7+16i is 7.

$$7$$