Solve (5-sqrt{-9})(-1+sqrt{-4})

$$( 5 - \sqrt { - 9 } ) ( - 1 + \sqrt { - 4 } )$$

Evaluate (complex solution)

$$1+13i$$

Solution Steps

Calculate the square root of -9 and get 3i.

$$\left(5-3i\right)\left(-1+\sqrt{-4}\right)$$

Calculate the square root of -4 and get 2i.

$$\left(5-3i\right)\left(-1+2i\right)$$

Multiply complex numbers 5-3i and -1+2i like you multiply binomials.

$$5\left(-1\right)+5\times \left(2i\right)-3i\left(-1\right)-3\times 2i^{2}$$

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

$$5\left(-1\right)+5\times \left(2i\right)-3i\left(-1\right)-3\times 2\left(-1\right)$$

Do the multiplications.

$$-5+10i+3i+6$$

Combine the real and imaginary parts.

$$-5+6+\left(10+3\right)i$$

Do the additions.

$$1+13i$$

Real Part (complex solution)

$$1$$

Solution Steps

Calculate the square root of -9 and get 3i.

$$Re(\left(5-3i\right)\left(-1+\sqrt{-4}\right))$$

Calculate the square root of -4 and get 2i.

$$Re(\left(5-3i\right)\left(-1+2i\right))$$

Multiply complex numbers 5-3i and -1+2i like you multiply binomials.

$$Re(5\left(-1\right)+5\times \left(2i\right)-3i\left(-1\right)-3\times 2i^{2})$$

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

$$Re(5\left(-1\right)+5\times \left(2i\right)-3i\left(-1\right)-3\times 2\left(-1\right))$$

Do the multiplications in 5\left(-1\right)+5\times \left(2i\right)-3i\left(-1\right)-3\times 2\left(-1\right).

$$Re(-5+10i+3i+6)$$

Combine the real and imaginary parts in -5+10i+3i+6.

$$Re(-5+6+\left(10+3\right)i)$$

Do the additions in -5+6+\left(10+3\right)i.

$$Re(1+13i)$$

The real part of 1+13i is 1.

$$1$$

Evaluate

$$\text{Indeterminate}$$