Complex numbers crossword

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Across
  1. 2. We need to multiply 2 cis(38) by 4 cis(107). What is the modulus of the result?
  2. 4. Every complex number has a real part and an __________ part.
  3. 6. Let z be a non-zero complex number. How many twelfth roots does z have in the complex plane?
  4. 8. What is the name of the diagram which enables us to show complex numbers
  5. 9. Suppose a + bi is a complex number. a- bi is called the complex __________ of a + bi.
  6. 12. What is (5 - i) + (2 + 4i)?
Down
  1. 1. What famous theorem about triangles is used to caluclate the modulus of a complex number?
  2. 3. Calculate the argument of 1 + 2i
  3. 5. What is the name of the theorem which enables calculation of powers of complex numbers in polar form?
  4. 7. A polynomial has real coefficients and 5 + i is a root. Give another root.
  5. 10. Consider the polynomial x^4 + 3x^3 - 5x^2 + 8. How many roots does it have in the complex plane (including any repeated roots)?
  6. 11. A complex number can be written in rectangular form or in _________ form.