DP Mathematics HL Questionbank

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Directly related questions

• 18M.1.hl.TZ2.7b: Find the value of the real part of $\frac{{z + w}}{{z - w}}$...
• 18M.1.hl.TZ2.7a: Find the real part of $\frac{{z + w}}{{z - w}}$.
• 16N.1.hl.TZ0.12d: Solve the inequality...
• 16N.1.hl.TZ0.12c: Find the values of $x$ that satisfy the equation $\left| p \right| = \left| q \right|$.
• 16N.1.hl.TZ0.12b: Show that $(\omega  - 3{\omega ^2})({\omega ^2} - 3\omega ) = 13$.
• 12M.1.hl.TZ1.7: Given that z is the complex number $x + {\text{i}}y$ and that...
• 12M.1.hl.TZ1.3: If ${z_1} = a + a\sqrt 3 i$ and ${z_2} = 1 - i$, where a is a real constant, express...
• 12M.1.hl.TZ2.6a: m and n are real numbers;
• 12M.1.hl.TZ2.6b: m and n are conjugate complex numbers.
• 12M.1.hl.TZ2.12A.a: Given that \({(x + {\text{i}}y)^2} = - 5 + 12{\text{i}},{\text{ }}x,{\text{ }}y \in...
• 12M.1.hl.TZ2.12A.c: For any complex number z , show that ${(z^*)^2} = ({z^2})^*$ .
• 12N.1.hl.TZ0.10a: (i)     Write down ${z_1}$ in Cartesian form. (ii)     Hence determine...
• 12N.2.hl.TZ0.10: Let $\omega = \cos \theta  + {\text{i}}\sin \theta$ . Find, in terms of $\theta$ , the...
• 08M.1.hl.TZ1.1: Express...
• 08M.2.hl.TZ1.10: Find, in its simplest form, the argument of...
• 08M.2.hl.TZ1.14: ${z_1} = {(1 + {\text{i}}\sqrt 3 )^m}{\text{ and }}{z_2} = {(1 - {\text{i}})^n}$ . (a)    ...
• 08M.2.hl.TZ2.9: Consider...
• 11M.1.hl.TZ2.4a: Find AB, giving your answer in the form $a\sqrt {b - \sqrt 3 }$ , where a ,...
• 11M.1.hl.TZ2.4b: Calculate ${\rm{A\hat OB}}$ in terms of $\pi$.
• 11M.1.hl.TZ2.12b: Let $\gamma = \frac{{1 + {\text{i}}\sqrt 3 }}{2}$. (i)     Show that $\gamma$ is one of the...
• 09M.1.hl.TZ1.1: Consider the complex numbers $z = 1 + 2{\text{i}}$ and $w = 2 + a{\text{i}}$ , where...
• 09M.1.hl.TZ1.13Part A: If z is a non-zero complex number, we define $L(z)$ by the...
• 09N.1.hl.TZ0.13a: Let $z = x + {\text{i}}y$ be any non-zero complex number. (i)     Express $\frac{1}{z}$ in...
• SPNone.2.hl.TZ0.4a: Find the modulus and argument of z , giving the argument in degrees.
• 13M.1.hl.TZ1.1a: If w = 2 + 2i , find the modulus and argument of w.
• 10M.2.hl.TZ1.4: (a)     Solve the equation ${z^3} = - 2 + 2{\text{i}}$, giving your answers in modulus-argument...
• 10M.2.hl.TZ2.9: Given that $z = \cos \theta + {\text{i}}\sin \theta$ show that (a)    ...
• 10N.1.hl.TZ0.11: Consider the complex number $\omega = \frac{{z + {\text{i}}}}{{z + 2}}$, where...
• 13M.1.hl.TZ2.7a: Write down the exact values of $\left| {{z_1}} \right|$ and $\arg ({z_2})$.
• 11N.2.hl.TZ0.6: The complex numbers ${z_1}$ and ${z_2}$ have arguments between 0 and $\pi$ radians. Given...
• 11N.2.hl.TZ0.10: Given that...
• 11N.2.hl.TZ0.14d: Hence, show that...
• 11M.1.hl.TZ1.2: Given that $\frac{z}{{z + 2}} = 2 - {\text{i}}$ , $z \in \mathbb{C}$ , find z in the form...
• 09N.1.hl.TZ0.2: Find the values of n such that ${\left( {1 + \sqrt 3 {\text{i}}} \right)^n}$ is a real number.
• 11M.1.hl.TZ1.13a: Write down the expansion of ${\left( {\cos \theta + {\text{i}}\sin \theta } \right)^3}$ in the...
• 14M.1.hl.TZ1.13: A geometric sequence $\left\{ {{u_n}} \right\}$, with complex terms, is defined by...
• 14M.1.hl.TZ2.7: Consider the complex numbers $u = 2 + 3{\text{i}}$ and $v = 3 + 2{\text{i}}$. (a)     Given...
• 13N.2.hl.TZ0.6: A complex number z is given by...
• 15M.2.hl.TZ1.12a: (i)     Use the binomial theorem to expand ${(\cos \theta  + {\text{i}}\sin \theta )^5}$. (ii)...