Q62.Let z = 1 + ai , be a complex number, a > 0, such that z3 is a real number. Then, the sum 1 + z + z2 + … . +z11 is equal to : (1) 1365 √3i (2) −1365 √3i (3) −1250 √3i (4) 1250 √3i
What This Question Tests
Tests the understanding of complex number properties, specifically how to determine 'a' such that z³ is real, and then sum a geometric progression involving the complex number z.
Concepts Tested
Formulas Used
(x+iy)^3 = x^3 - 3xy^2 + i(3x^2y - y^3)
Sum of GP: S_n = a(r^n - 1)/(r - 1)
📚 NCERT Sections This Tests
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Powers of complex numbers
- Year
- 2016
- Shift
- 10 Apr Online
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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