Modulus, Argument and Polar Form Worksheet with Answer Key

What's on the worksheet

1. Write each number in the form a + bi, exactly.
2. Write each number in polar form rcisθ, with the modulus exact and θ the exact principal argument.
   -5 + 5i4\sqrt{3} - 4i-3\sqrt{2} + \sqrt{6}\,i\dfrac{-12}{i}-3i(1 + i)
3. None of these is in polar form with the principal argument.
   4\left(\cos\dfrac{19\pi}{6} - i\sin\dfrac{19\pi}{6}\right)-5\operatorname{cis}\dfrac{7\pi}{3}2\left(\sin\dfrac{\pi}{5} + i\cos\dfrac{\pi}{5}\right)-6\left(\cos\dfrac{2\pi}{7} - i\sin\dfrac{2\pi}{7}\right)
4. Write z = (2 - 3i)² in the form a + bi.
5. Let z = -52 - 5√(3)2\,i.
7. Let k be a nonzero real number and z = -k + k√(3)\,i.