Download App

STD 11 - 4.1 complex nubers — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.1 complex nubers4 Marks
MCQ
The locus represented by $|z - 1| = |z + i|$ is
  • A
    A circle of radius $1$
  • B
    An ellipse with foci at $(1,\,0)$ and $(0, -1)$
  • ✓
    A straight line through the origin
  • D
    A circle on the line joining $(1,\,0),(0,\,1)$ as diameter
✓

Answer

Correct option: C.
A straight line through the origin
c
(c) $|z - 1|\, = \,|z + i|$ ==> $|x - 1 + iy{|^2} = \,|x + i(y + 1){|^2}$
==> ${(x - 1)^2} + {y^2} = {x^2} + {(y + 1)^2}$
==> $x + y = 0$ i.e., a straight line through the origin.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $(2, 0)$ is the vertex and $y$ - axis the directrix of a parabola, then its focus is
→
A test consists of $6$ multiple choice questions, each having $4$ alternative ans wers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is
→
$\mathop {\lim }\limits_{x \to 0} \frac{{{y^2}}}{x} = ........$, where ${y^2} = ax + b{x^2} + c{x^3}$
→
If $\omega $ is an imaginary cube root of unity, ${(1 + \omega - {\omega ^2})^7}$equals
→
Let $2\hat a = \hat b \times \hat c + 2\hat b$ then sum of possible value$(s)$ .of $\left| {2\hat a + \hat b + \hat c} \right|$ is
→
$\int_{}^{} {\frac{{\cos 2x - \cos 2\alpha }}{{\cos x - \cos \alpha }}} dx = $
→
If the second term of the expansion ${\left[ {{a^{\frac{1}{{13}}}}\,\, + \,\,\frac{a}{{\sqrt {{a^{ - 1}}} }}} \right]^n}$ is $14a^{5/2}$ then the value of $\frac{{^n{C_3}}}{{^n{C_2}}}$ is :
→
A purse contains $4$ copper coins and $3$ silver coins. A second purse contains $6$ copper coins and $4$ silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?
→
For $0<\theta<\pi / 2$, if the eccentricity of the hyperbola $\mathrm{x}^2-\mathrm{y}^2 \operatorname{cosec}^2 \theta=5$ is $\sqrt{7}$ times eccentricity of the ellipse $x^2 \operatorname{cosec}^2 \theta+y^2=5$, then the value of $\theta$ is :
→
Given the relation $R = \{(1, 2), (2, 3)\}$ on the set $A = {1, 2, 3}$, the minimum number of ordered pairs which when added to $R$ make it an equivalence relation is
→