Write each expression in the form \(a+bi\), where \(a\) and \(b\) are real numbers:

1. \(\frac{5 \pm \sqrt{\text-4}}{3}\)
2. \(\frac{10 \pm \sqrt{\text-16}}{2}\)
3. \(\frac{\text-3 \pm \sqrt{\text-144}}{6}\)

Priya is using the quadratic formula to solve two different quadratic equations.

For the first equation, she writes \(x= \frac{4 \pm \sqrt{16-72}}{12}\)

For the second equation, she writes \(x=\frac{8 \pm \sqrt{64-24}}{6}\)

Which equation(s) has real solutions? Which equation(s) has non-real solutions? Explain how you know.

Find the exact real solution(s) to each of these equations, or explain why there is no solution.

1. \(x^2=25\)
2. \(x^3 = 27\)
3. \(x^2=12\)
4. \(x^3=12\)

Kiran is solving the equation \(\sqrt{x+2} - 5 = 11\) and decides to start by squaring both sides. Which equation results if Kiran squares both sides as his first step?

Plot each number on the real or imaginary number line.

1. \(\text-\sqrt{4}\)
2. \(\sqrt{\text-1}\)
3. \(3\sqrt{4}\)
4. \(\text-3\sqrt{\text-1}\)
5. \(4\sqrt{\text-1}\)
6. \(2\sqrt{2}\)