Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Complex Numbers question

2021 · 22 Jul · Shift 2 · Q34
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Main
  3. /Mathematics
  4. /Complex Numbers
  5. /2021 · 22 Jul · Shift 2 · Q34

Complex Numbers question

2021 · 22 Jul · Shift 2 · Q34

JEE MainMathematicsComplex NumbersMCQ+4 / −1
Let n denote the number of solutions of the equation z2 + 3 z‾\overline zz= 0, where z is a complex number. Then the value of ∑k=0∞1nk\sum\limits_{k = 0}^\infty {{1 \over {{n^k}}}}k=0∑∞​nk1​ is equal to :
  1. A
    1
  2. B
    43{4 \over 3}34​
  3. C
    32{3 \over 2}23​
  4. D
    2
PreviousNext

More from Complex Numbers

  • If the least and the largest real values of a, for which the equation z + α|z – 1| + 2i = 0 (z ∈ C and i = −1​) has a solution, are p and q respectively; then 4(p2 + q2) is equal to ​.2021 · Numerical
  • Let i=−1​. If (1−i)24(−1+i3​)21​+(1+i)24(1+i3​)21​=k, and n=[∣k∣] be the greatest integral part of | k |. Then…2021 · Numerical
  • Let the lines (2 − i)z = (2 + i) z and (2 + i)z + (i − 2) z− 4i = 0, (here i2 =− 1) be normal to a circle C. If the line iz + z + 1 + i = 0 is tangent to this circle C, then its radius is :2021 · MCQ
  • If α, β∈ R are such that 1 − 2i (here i2 =− 1) is a root of z2 + α z + β = 0, then (α−β) is equal to :2021 · MCQ
  • Let S={n∈N​(01​i0​)n(ac​bd​)=(ac​bd​)∀a,b,c,d∈R}…2021 · Numerical
  • The equation of a circle is Re(z2) + 2(Im(z))2 + 2Re(z) = 0, where z = x + iy. A line which passes through the center of the given circle and the vertex of the parabola, x2 − 6x − y + 13 = 0, has y-intercept equal to ​…2021 · Numerical
  • The equation arg(z+1z−1​)=4π​ represents a circle with :2021 · MCQ
  • Let z=21−i3​​, i=−1​. Then the value of 21+(z+z1​)3+(z2+z21​)3+(z3+z31​)3+....+(z21+z211​)3…2021 · Numerical