Question:
If z is a complex number then $|z+1|=\sqrt3|z-1|$ represents
If z is a complex number then $|z+1|=\sqrt3|z-1|$ represents
Updated On: Jul 6, 2022
- Straight line
- Ellipse
- Hyperbola
- circle
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The Correct Option is D
Solution and Explanation
$\left|z+1\right|^{2}=3\left|z-1\right|^{2}$
$\Rightarrow \left(x+1\right)^{2}+y^{2}=3\left[\left(x-1\right)^{2}+y^{2}\right]$
$\Rightarrow 2\left(x^{2}+y^{2}\right)-8x+2=0$
$\Rightarrow x^{2}+y^{2}-4x+1=0$ which is a circle.
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
