Solve (130+59.15i)(30+13.65i)

$$( 130 + 59.15 i ) ( 30 + 13.65 i )$$

Evaluate

$$3092.6025+3549i$$

Solution Steps

Multiply complex numbers 130+59.15i and 30+13.65i like you multiply binomials.

$$130\times 30+130\times \left(13.65i\right)+59.15i\times 30+59.15\times 13.65i^{2}$$

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

$$130\times 30+130\times \left(13.65i\right)+59.15i\times 30+59.15\times 13.65\left(-1\right)$$

Do the multiplications.

$$3900+1774.5i+1774.5i-807.3975$$

Combine the real and imaginary parts.

$$3900-807.3975+\left(1774.5+1774.5\right)i$$

Do the additions.

$$3092.6025+3549i$$

Real Part

$$3092.6025$$

Solution Steps

Multiply complex numbers 130+59.15i and 30+13.65i like you multiply binomials.

$$Re(130\times 30+130\times \left(13.65i\right)+59.15i\times 30+59.15\times 13.65i^{2})$$

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

$$Re(130\times 30+130\times \left(13.65i\right)+59.15i\times 30+59.15\times 13.65\left(-1\right))$$

Do the multiplications in 130\times 30+130\times \left(13.65i\right)+59.15i\times 30+59.15\times 13.65\left(-1\right).

$$Re(3900+1774.5i+1774.5i-807.3975)$$

Combine the real and imaginary parts in 3900+1774.5i+1774.5i-807.3975.

$$Re(3900-807.3975+\left(1774.5+1774.5\right)i)$$

Do the additions in 3900-807.3975+\left(1774.5+1774.5\right)i.

$$Re(3092.6025+3549i)$$

The real part of 3092.6025+3549i is 3092.6025.

$$3092.6025$$