DP Mathematics HL Questionbank

Description

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 $\alpha$.