New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2003 · Shift 0 · Q98

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Complex Numbers
2003 · Shift 0 · Q98

Complex Numbers question

2003 · Shift 0 · Q98

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

{Z_1}

and

{Z_2}

be two roots of the equation

{Z^2} + aZ + b = 0

, Z being complex. Further , assume that the origin,

{Z_1}

and

{Z_2}

form an equilateral triangle. Then :

A
${a^2} = 4b$
B
${a^2} = b$
C
${a^2} = 2b$
D
${a^2} = 3b$

More from Complex Numbers

If $(\frac{1 + i}{1 - i})^{x} = 1$ then :2003 · MCQ
z and w are two nonzero complex numbers such that $∣ z ∣ = ∣ w ∣$ and Arg z + Arg w = $π$ then z equals2002 · MCQ
If $∣ z - 4 ∣ < ∣ z - 2 ∣$ , its solution is given by :2002 · MCQ
The locus of the centre of a circle which touches the circle $∣ z - z_{1} ∣ = a$ and $∣ z - z_{2} ∣ = b$ externally ( $z, z_{1} & z_{2}$ are complex numbers) will be :2002 · MCQ
Let $z$ be a complex number such that $∣ z ∣ = 1$ . If $\frac{2 + k ^{2} z}{k + z ˉ} = k z, k \in R$ , then the maximum distance of $k + i k^{2}$ from the circle $∣ z - (1 + 2 i) ∣ = 1$ is :2025 · MCQ
Let $z \in C$ be such that $\frac{z ^{2} + 3 i}{z - 2 + i} = 2 + 3 i$ . Then the sum of all possible values of $z^{2}$ is :2025 · MCQ
If $z_{1}, z_{2}, z_{3} \in C$ are the vertices of an equilateral triangle, whose centroid is $z_{0}$ , then $k = 1 \sum 3 (z_{k} - z_{0})^{2}$ is equal to2025 · MCQ
Let $A = {z \in C : ∣ z - 2 - i ∣ = 3}, B = {z \in C : Re (z - i z) = 2}$ and $S = A \cap B$ . Then $\sum_{z \in S} ∣ z ∣^{2}$ is equal to .2025 · Numerical