Solve (sqrt{3}-2i)-i[2-i(sqrt{3}+4)]

$$( \sqrt { 3 } - 2 i ) - i [ 2 - i ( \sqrt { 3 } + 4 ) ]$$

Real Part

$$-4$$

Solution Steps

Use the distributive property to multiply -i by \sqrt{3}+4.

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

Use the distributive property to multiply -i by 2-i\sqrt{3}-4i.

$$Re(\sqrt{3}-2i-2i-\sqrt{3}-4)$$

Combine the real and imaginary parts in -2i-2i-4.

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

Add -2 to -2.

$$Re(\sqrt{3}-\sqrt{3}-4-4i)$$

Combine \sqrt{3} and -\sqrt{3} to get 0.

$$Re(-4-4i)$$

The real part of -4-4i is -4.

$$-4$$

Evaluate

$$-4-4i$$