DP Mathematics HL Questionbank
\(n\)th roots of a complex number.
Description
[N/A]Directly related questions
- 16M.1.hl.TZ2.12c: Write down the roots of the equation \({z^7} - 1 = 0,{\text{ }}z \in \mathbb{C}\) in terms of...
- 16M.1.hl.TZ2.12b: (i) Expand \((w - 1)(1 + w + {w^2} + {w^3} + {w^4} + {w^5} + {w^6})\). (ii) Hence deduce...
- 16M.1.hl.TZ2.12a: Verify that \(w\) is a root of the equation \({z^7} - 1 = 0,{\text{ }}z \in \mathbb{C}\).
- 16N.1.hl.TZ0.12a: Determine the value of (i) \(1 + \omega + {\omega ^2}\); (ii) ...
- 17N.1.hl.TZ0.8: Determine the roots of the equation \({(z + 2{\text{i}})^3} = 216{\text{i}}\),...
- 12M.1.hl.TZ2.12A.b: Hence find the two square roots of \( - 5 + 12{\text{i}}\) .
- 12M.1.hl.TZ2.12A.d: Hence write down the two square roots of \( - 5 - 12{\text{i}}\) .
- 12N.1.hl.TZ0.10c: Let \(z = r\,{\text{cis}}\theta \) , where \(r \in {\mathbb{R}^ + }\) and...
- 12N.1.hl.TZ0.10b: (i) Write \({z_2}\) in modulus-argument form. (ii) Hence solve the equation...
- 12N.1.hl.TZ0.10d: Find the smallest positive value of n for which...
- 08N.1.hl.TZ0.13Part A: (a) Use de Moivre’s theorem to find the roots of the equation \({z^4} = 1 - {\text{i}}\)...
- 10M.2.hl.TZ1.4: (a) Solve the equation \({z^3} = - 2 + 2{\text{i}}\), giving your answers in modulus-argument...
- 15M.1.hl.TZ2.7a: Find three distinct roots of the equation \(8{z^3} + 27 = 0,{\text{ }}z \in \mathbb{C}\) giving...
- 15N.1.hl.TZ0.11a: Solve the equation \({z^3} = 8{\text{i}},{\text{ }}z \in \mathbb{C}\) giving your answers in the...
- 15M.2.hl.TZ1.12b: Find the value of \(r\) and the value of \(\alpha \).
