DP Mathematics HL Questionbank

Modulus–argument (polar) form z=r(cosθ+isinθ)=rcisθ=reiθz=r(cosθ+isinθ)=rcisθ=reiθ
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[N/A]Directly related questions
- 18M.2.hl.TZ2.1c: Find the argument of zz, giving your answer to 4 decimal places.
- 18M.2.hl.TZ2.1b: Find the exact value of the modulus of zz.
- 18M.2.hl.TZ2.1a: Express zz in the form a+iba+ib, where a,b∈Q.
- 18M.1.hl.TZ1.11a.ii: Sketch on an Argand diagram the points represented by w0 , w1 , w2 and w3.
- 18M.1.hl.TZ1.11a.i: Express w2 and w3 in modulus-argument form.
- 12M.1.hl.TZ1.3: If z1=a+a√3i and z2=1−i, where a is a real constant, express...
- 12M.1.hl.TZ2.12B.e: Express each of the four roots of the equation in the form reiθ .
- 12N.1.hl.TZ0.10c: Let z=rcisθ , where r∈R+ and...
- 12N.1.hl.TZ0.10b: (i) Write z2 in modulus-argument form. (ii) Hence solve the equation...
- 09M.1.hl.TZ2.7: Given that z1=2 and z2=1+√3i are roots of the cubic equation...
- SPNone.1.hl.TZ0.10a: Calculate z1z2 giving your answer both in modulus-argument form and...
- SPNone.1.hl.TZ0.10b: Using your results, find the exact value of tan 75° , giving your answer in the form...
- 10M.1.hl.TZ2.13: Consider...
- 10M.2.hl.TZ1.4: (a) Solve the equation z3=−2+2i, giving your answers in modulus-argument...
- 11N.2.hl.TZ0.14a: Show that |eiθ|=1.
- 13M.1.hl.TZ2.13a: (i) Express each of the complex numbers...
- 13M.1.hl.TZ2.13b: (i) State the solutions of the equation z7=1 for z∈C, giving them...
- 12N.1.hl.TZ0.10d: Find the smallest positive value of n for which...
- 09N.1.hl.TZ0.2: Find the values of n such that (1+√3i)n is a real number.
- 14M.1.hl.TZ2.7: Consider the complex numbers u=2+3i and v=3+2i. (a) Given...
- 14M.2.hl.TZ2.13d: Find the area of triangle OA′B′.
- 14M.2.hl.TZ2.13b: Given u=1+√3i and v=1−i, (i) express u and v...
- 13N.1.hl.TZ0.12d: Show that...
- 14M.2.hl.TZ2.13a: Consider z=r(cosθ+isinθ), z∈C. Use...
- 14M.2.hl.TZ2.13c: Plot point A and point B on the Argand diagram.
- 13N.1.hl.TZ0.12c: Hence show that cos4θ=pcos4θ+qcos2θ+r, where...
- 15N.1.hl.TZ0.11a: Solve the equation z3=8i, z∈C giving your answers in the...
- 15N.1.hl.TZ0.11b: Consider the complex numbers z1=1+i and...