If z and w are complex numbers satisfying ((z-2 i)/(z+2))=(π)/(4) and ((w-2 i)/(w+2))=(π)/(2) re

step 1 In this question, there are two complex number, Z and W. Z satisfies argument z minus 2 aota upo

If z and w are complex numbers satisfying ((z-2...

If $z$ and $w$ are complex numbers satisfying $\arg \left(\frac{z-2 i}{z+2}\right)=\frac{\pi}{4}$ and $\arg \left(\frac{w-2 i}{w+2}\right)=\frac{\pi}{2}$ respectively, then, the intersection of the locus of $z$ and the locus of $w$ is the (a) straight line joining $(0,2)$ and $(-2,0)$ (b) set containing the points $(0,2)$ and $(-2,0)$ (c) circle passing through the points $(0,2)$ and $(-2,0)$ (d) empty set

If $z$ and $w$ are complex numbers satisfying $\arg \left(\frac{z-2 i}{z+2}\right)=\frac{\pi}{4}$ and $\arg \left(\frac{w-2 i}{w+2}\right)=\frac{\pi}{2}$ respectively, then, the intersection of the locus of $z$ and the locus of $w$ is the
(a) straight line joining $(0,2)$ and $(-2,0)$
(b) set containing the points $(0,2)$ and $(-2,0)$
(c) circle passing through the points $(0,2)$ and $(-2,0)$
(d) empty set

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Complex Numbers in the Plane

Complex numbers can be represented as points in the complex plane with real and imaginary parts corresponding to horizontal and vertical coordinates, respectively. This geometric representation allows for the interpretation of algebraic operations, such as addition, multiplication, and the determination of arguments, in a visual manner.

Argument of a Complex Number

The argument of a complex number is the angle measured from the positive real axis to the line joining the origin to the complex number. It is a key concept when relating algebraic conditions to geometric loci, particularly in problems where ratios of complex numbers are considered.

Loci Defined by Complex Conditions

A locus in the complex plane is a set of all points that satisfy a given condition, often expressed in terms of modulus or argument constraints. Such loci might represent circles, lines, or other curves, depending on the nature of the condition provided.

Intersection of Geometric Loci

The intersection of loci refers to the set of points that simultaneously satisfy multiple geometric conditions or equations. Determining this intersection involves analyzing and combining the individual constraints to identify the common solutions.

Transcript

Please give Ace some feedback