If the amplitude of $z - 2 - 3i$ is $\frac{\pi }{4}$, then the locus of $z = x + iy$, is

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

If the amplitude of

z - 2 - 3i

\frac{\pi }{4}

, then the locus of

z = x + iy

, is

View answer and explanation

Correct option: D

x - y + 1 = 0

Option D (

x - y + 1 = 0

) is correct because it represents the locus of z, derived from the given amplitude condition by equating the tangent of the angle to 1.

Practice All Chapter MCQs →

{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

z, \frac{z}{1-z^2}

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

\left|\sum\limits_{r=1}^n z_r\right|

(z+a b)^3=a^3

a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}