Solve 1-(2-sqrt{-9})(sqrt{-4}+3)

$$1 - ( 2 - \sqrt { - 9 } ) ( \sqrt { - 4 } + 3 )$$

Evaluate (complex solution)

$$-11+5i$$

Solution Steps

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

$$1-\left(2-3i\right)\left(\sqrt{-4}+3\right)$$

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

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

Multiply -1 and 2-3i to get -2+3i.

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

Use the distributive property to multiply -2+3i by 2i+3.

$$1+\left(-6-4i\right)+\left(-6+9i\right)$$

Combine the real and imaginary parts in numbers -6-4i and -6+9i.

$$1-6-6+\left(-4+9\right)i$$

Add -6 to -6. Add -4 to 9.

$$1+\left(-12+5i\right)$$

Combine the real and imaginary parts in numbers 1 and -12+5i.

$$1-12+5i$$

Add 1 to -12.

$$-11+5i$$

Real Part (complex solution)

$$-11$$

Solution Steps

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

$$Re(1-\left(2-3i\right)\left(\sqrt{-4}+3\right))$$

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

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

Multiply -1 and 2-3i to get -2+3i.

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

Use the distributive property to multiply -2+3i by 2i+3.

$$Re(1+\left(-6-4i\right)+\left(-6+9i\right))$$

Combine the real and imaginary parts in numbers -6-4i and -6+9i.

$$Re(1-6-6+\left(-4+9\right)i)$$

Add -6 to -6. Add -4 to 9.

$$Re(1+\left(-12+5i\right))$$

Combine the real and imaginary parts in numbers 1 and -12+5i.

$$Re(1-12+5i)$$

Add 1 to -12.

$$Re(-11+5i)$$

The real part of -11+5i is -11.

$$-11$$

Evaluate

$$\text{Indeterminate}$$