Solve (5-6i)(6+5i)

$$( 5 - 6 i ) ( 6 + 5 i )$$

Evaluate

$$60-11i$$

Solution Steps

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

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

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

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

Do the multiplications.

$$30+25i-36i+30$$

Combine the real and imaginary parts.

$$30+30+\left(25-36\right)i$$

Do the additions.

$$60-11i$$

Real Part

$$60$$

Solution Steps

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

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

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

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

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

$$Re(30+25i-36i+30)$$

Combine the real and imaginary parts in 30+25i-36i+30.

$$Re(30+30+\left(25-36\right)i)$$

Do the additions in 30+30+\left(25-36\right)i.

$$Re(60-11i)$$

The real part of 60-11i is 60.

$$60$$