Imaginary and Complex Numbers Worksheet with Answer Key

What's on the worksheet

1. Write each number as a multiple of i, with any root simplified.
   5\sqrt{-36}2\sqrt{-63}\sqrt{-\frac{12}{49}}-\dfrac{1}{2}\sqrt{-200}
2. Write each number in standard form, then give its real and imaginary parts.
   8 + \sqrt{-49}\sqrt{-16} - \sqrt{25}-\sqrt{-75}i^2 - 4i
3. Write each number in standard form and say if it is real, imaginary or pure imaginary.
   i^6\sqrt{-5}1 + \sqrt{-5}\cdot\sqrt{-20}\sqrt{2} - \sqrt{-2}\dfrac{\sqrt{-50}}{5}
4. Simplify, writing any answer that is not real in standard form.
   (4i)^2(-i\sqrt{2})^4(i^3)^7i^{30} + i^{3}(2i)^3 \cdot i
5. Find the real numbers x and y that match the real and imaginary parts.
6. Solve an equation over the complex numbers.
7. Decide whether each statement about products of square roots of negatives is true.
8. Find a power of i that equals minus i, and show a sum of powers is zero.