DP Mathematics HL Questionbank
1.5
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Description
[N/A]Directly related questions
- 18M.1.hl.TZ2.7b: Find the value of the real part of z+wz−w...
- 18M.1.hl.TZ2.7a: Find the real part of z+wz−w.
- 16N.1.hl.TZ0.12d: Solve the inequality...
- 16N.1.hl.TZ0.12c: Find the values of x that satisfy the equation |p|=|q|.
- 16N.1.hl.TZ0.12b: Show that (ω−3ω2)(ω2−3ω)=13.
- 15N.1.hl.TZ0.11b: Consider the complex numbers z1=1+i and...
- 12M.1.hl.TZ1.3: If z1=a+a√3i and z2=1−i, where a is a real constant, express...
- 12M.1.hl.TZ1.7: Given that z is the complex number x+iy and that...
- 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=(z2)∗ .
- 12N.1.hl.TZ0.10a: (i) Write down z1 in Cartesian form. (ii) Hence determine...
- 12N.2.hl.TZ0.10: Let ω=cosθ+isinθ . Find, in terms of θ , 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: z1=(1+i√3)m and z2=(1−i)n . (a) ...
- 08M.2.hl.TZ2.9: Consider...
- 08N.1.hl.TZ0.13Part B: (a) Expand and simplify (x−1)(x4+x3+x2+x+1) . (b) Given that b is...
- 11M.1.hl.TZ2.4a: Find AB, giving your answer in the form a√b−√3 , where a ,...
- 11M.1.hl.TZ2.4b: Calculate AˆOB in terms of π.
- 11M.1.hl.TZ2.12b: Let γ=1+i√32. (i) Show that γ is one of the...
- 09M.1.hl.TZ1.1: Consider the complex numbers z=1+2i and w=2+ai , 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+iy be any non-zero complex number. (i) Express 1z 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.1.hl.TZ2.13: Consider...
- 10M.2.hl.TZ1.4: (a) Solve the equation z3=−2+2i, giving your answers in modulus-argument...
- 10M.2.hl.TZ2.9: Given that z=cosθ+isinθ show that (a) ...
- 10N.1.hl.TZ0.11: Consider the complex number ω=z+iz+2, where...
- 13M.1.hl.TZ2.7a: Write down the exact values of |z1| and arg(z2).
- 11N.2.hl.TZ0.6: The complex numbers z1 and z2 have arguments between 0 and π radians. Given...
- 11N.2.hl.TZ0.10: Given that...
- 11N.2.hl.TZ0.14d: Hence, show that...
- 11M.1.hl.TZ1.2: Given that zz+2=2−i , z∈C , find z in the form...
- 09N.1.hl.TZ0.2: Find the values of n such that (1+√3i)n is a real number.
- 11M.1.hl.TZ1.13a: Write down the expansion of (cosθ+isinθ)3 in the...
- 14M.1.hl.TZ1.13: A geometric sequence {un}, with complex terms, is defined by...
- 14M.1.hl.TZ2.7: Consider the complex numbers u=2+3i and v=3+2i. (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 (cosθ+isinθ)5. (ii)...
Sub sections and their related questions
Complex numbers: the number i=√−1 ; the terms real part, imaginary part, conjugate, modulus and argument.
- 12M.1.hl.TZ1.3: If z1=a+a√3i and z2=1−i, where a is a real constant, express...
- 12M.1.hl.TZ1.7: Given that z is the complex number x+iy and that...
- 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=(z2)∗ .
- 12N.1.hl.TZ0.10a: (i) Write down z1 in Cartesian form. (ii) Hence determine...
- 12N.2.hl.TZ0.10: Let ω=cosθ+isinθ . Find, in terms of θ , 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: z1=(1+i√3)m and z2=(1−i)n . (a) ...
- 08M.2.hl.TZ2.9: Consider...
- 11M.1.hl.TZ2.4a: Find AB, giving your answer in the form a√b−√3 , where a ,...
- 11M.1.hl.TZ2.4b: Calculate AˆOB in terms of π.
- 11M.1.hl.TZ2.12b: Let γ=1+i√32. (i) Show that γ is one of the...
- 09M.1.hl.TZ1.1: Consider the complex numbers z=1+2i and w=2+ai , where...
- 09M.1.hl.TZ1.13Part A: If z is a non-zero complex number, we define L(z) by the...
- 09N.1.hl.TZ0.2: Find the values of n such that (1+√3i)n is a real number.
- 09N.1.hl.TZ0.13a: Let z=x+iy be any non-zero complex number. (i) Express 1z 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 z3=−2+2i, giving your answers in modulus-argument...
- 10M.2.hl.TZ2.9: Given that z=cosθ+isinθ show that (a) ...
- 10N.1.hl.TZ0.11: Consider the complex number ω=z+iz+2, where...
- 13M.1.hl.TZ2.7a: Write down the exact values of |z1| and arg(z2).
- 11N.2.hl.TZ0.6: The complex numbers z1 and z2 have arguments between 0 and π radians. Given...
- 11N.2.hl.TZ0.10: Given that...
- 11N.2.hl.TZ0.14d: Hence, show that...
- 11M.1.hl.TZ1.2: Given that zz+2=2−i , z∈C , find z in the form...
- 11M.1.hl.TZ1.13a: Write down the expansion of (cosθ+isinθ)3 in the...
- 14M.1.hl.TZ1.13: A geometric sequence {un}, with complex terms, is defined by...
- 14M.1.hl.TZ2.7: Consider the complex numbers u=2+3i and v=3+2i. (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 (cosθ+isinθ)5. (ii)...
- 16N.1.hl.TZ0.12b: Show that (ω−3ω2)(ω2−3ω)=13.
- 16N.1.hl.TZ0.12c: Find the values of x that satisfy the equation |p|=|q|.
- 16N.1.hl.TZ0.12d: Solve the inequality...
- 18M.1.hl.TZ2.7a: Find the real part of z+wz−w.
- 18M.1.hl.TZ2.7b: Find the value of the real part of z+wz−w...
Cartesian form z=a+ib .
- 12M.1.hl.TZ1.3: If z1=a+a√3i and z2=1−i, where a is a real constant, express...
- 12M.1.hl.TZ1.7: Given that z is the complex number x+iy and that...
- 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=(z2)∗ .
- 12N.1.hl.TZ0.10a: (i) Write down z1 in Cartesian form. (ii) Hence determine...
- 11M.1.hl.TZ2.12b: Let γ=1+i√32. (i) Show that γ is one of the...
- 10M.2.hl.TZ1.4: (a) Solve the equation z3=−2+2i, giving your answers in modulus-argument...
- 11M.1.hl.TZ1.2: Given that zz+2=2−i , z∈C , find z in the form...
- 11M.1.hl.TZ1.13a: Write down the expansion of (cosθ+isinθ)3 in the...
- 15N.1.hl.TZ0.11b: Consider the complex numbers z1=1+i and...
Sums, products and quotients of complex numbers.
- 12M.1.hl.TZ1.3: If z1=a+a√3i and z2=1−i, where a is a real constant, express...
- 12M.1.hl.TZ1.7: Given that z is the complex number x+iy and that...
- 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=(z2)∗ .
- 12N.1.hl.TZ0.10a: (i) Write down z1 in Cartesian form. (ii) Hence determine...
- 08N.1.hl.TZ0.13Part B: (a) Expand and simplify (x−1)(x4+x3+x2+x+1) . (b) Given that b is...
- 11M.1.hl.TZ2.12b: Let γ=1+i√32. (i) Show that γ is one of the...
- 10M.1.hl.TZ2.13: Consider...
- 11M.1.hl.TZ1.2: Given that zz+2=2−i , z∈C , find z in the form...
- 11M.1.hl.TZ1.13a: Write down the expansion of (cosθ+isinθ)3 in the...
- 15N.1.hl.TZ0.11b: Consider the complex numbers z1=1+i and...
- 16N.1.hl.TZ0.12b: Show that (ω−3ω2)(ω2−3ω)=13.
- 16N.1.hl.TZ0.12c: Find the values of x that satisfy the equation |p|=|q|.
- 16N.1.hl.TZ0.12d: Solve the inequality...
- 18M.1.hl.TZ2.7a: Find the real part of z+wz−w.
- 18M.1.hl.TZ2.7b: Find the value of the real part of z+wz−w...