DP Mathematics HL Questionbank

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Directly related questions

• 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...
• 11M.1.hl.TZ2.12b: Let \(\gamma = \frac{{1 + {\text{i}}\sqrt 3 }}{2}\). (i)     Show that \(\gamma \) is one of the...
• 11M.1.hl.TZ1.2: Given that \(\frac{z}{{z + 2}} = 2 - {\text{i}}\) , \(z \in \mathbb{C}\) , find z in the form...
• 10M.2.hl.TZ1.4: (a)     Solve the equation \({z^3} = - 2 + 2{\text{i}}\), giving your answers in modulus-argument...
• 11M.1.hl.TZ1.13a: Write down the expansion of \({\left( {\cos \theta + {\text{i}}\sin \theta } \right)^3}\) in the...
• 15N.1.hl.TZ0.11b: Consider the complex numbers \({z_1} = 1 + {\text{i}}\) and...