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Modulus of complex number and its Properties - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Modulus of complex number and its Properties is considered one the most difficult concept.
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39 Questions around this concept.
Solve by difficulty
If $\mathrm{S}=\{\mathrm{z} \in \mathrm{C}:|\mathrm{z}-\mathrm{i}|=|\mathrm{z}+\mathrm{i}|=|\mathrm{z}-1|\}$, then, $\mathrm{n}(\mathrm{S})$ is :
Concepts Covered - 1
Modulus of complex number and its Properties
If z = x + iy is a complex number. Then, the modulus of z, denoted by | z |, is the distance of z from origin in Argand plane, and it is a non-negative real number equal to .
i.e. |z| =.
Every complex number can be represented as a point in the argand plane with x-axis as real axis and y-axis as imaginary axis.
(length r from origin to point (x,y))
Properties of Modulus
i) |z| ≥ 0
ii) |z| = 0, iff z = 0 and |z| >0, iff z ≠ 0
iii) -|z| ≤ Re(z) ≤ |z| and -|z| ≤ Im(z) ≤ |z|
iv)
v)
vi)
vii)
viii) (Triangle inequality) this can be generalised for n complex numbers.
ix)
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