>
Exams
>
Mathematics
>
complex numbers
>
the modulus of the complex number 1 i 2 1 3i 2 6i
Question:
The modulus of the complex number
\(\frac{(1+i)^2(1+3i)}{(2-6i)(2-2i)}\)
is
KCET - 2023
KCET
Updated On:
Nov 27, 2024
\(\frac{1}{\sqrt2}\)
\(\frac{4}{\sqrt2}\)
\(\frac{\sqrt2}{4}\)
\(\frac{2}{\sqrt2}\)
Hide Solution
Verified By Collegedunia
The Correct Option is
C
Solution and Explanation
The correct answer is (C) :
\(\frac{\sqrt2}{4}\)
.
Download Solution in PDF
Was this answer helpful?
10
10
Top Questions on complex numbers
If
\(r = |z|,\ θ = arg(z)\)
and
\( z = 2 – 2\ tan (\frac {5\pi}{8})\)
then find
\((r, θ)\)
.
JEE Main - 2024
Mathematics
complex numbers
View Solution
If $z$ is a complex number such that $|z| \geq 1$, then the minimum value of \[\left| z + \frac{1}{2}(3 + 4i) \right|\]is:
JEE Main - 2024
Mathematics
complex numbers
View Solution
Let $z$ be a complex number such that $|z + 2| = 1$ and $\text{Im}\left(\frac{z+1}{z+2}\right) = \frac{1}{5}$. Then the value of $|\text{Re}(z+2)|$ is:
JEE Main - 2024
Mathematics
complex numbers
View Solution
The sum of all possible values of \(\theta \in [-\pi, 2\pi]\), for which \[ \frac{1 + i \cos\theta}{1 - 2i \cos\theta} \] is purely imaginary, is equal to:
JEE Main - 2024
Mathematics
complex numbers
View Solution
If $z_1, z_2$ are two distinct complex numbers such that \[ \frac{|z_1 - 2z_2|}{\left| \frac{1}{2} - z_1 \overline{z_2} \right|} = 2, \] then
JEE Main - 2024
Mathematics
complex numbers
View Solution
View More Questions
Questions Asked in KCET exam
The speed of sound in an ideal gas at a given temperature T is v. The rms speed of gas molecules at that temperature is v
rms
. The ratio of the velocities v and v
rms
for helium and oxygen gases are X and X' respectively. Then
\(\frac{X}{X'}\)
is equal to
KCET - 2023
Thermodynamics
View Solution
If
\(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\)
are in A.P., then p, q, r
KCET - 2023
Arithmetic Progression
View Solution
A stretched wire of a material whose Young's modulus Y = 2 × 10
11
Nm
-2
has Poisson's ratio of 0.25. Its lateral strain ε
l
= 10
-3
. The elastic energy density of the wire is
KCET - 2023
mechanical properties of solids
View Solution
A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field B
H
= 3 × 10
-5
T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms
-2
)
KCET - 2023
Faradays laws of induction
View Solution
A 60 W source emits monochromatic light of wavelength 662.5 nm. The number of photons emitted per second is
KCET - 2023
Quantum Physics
View Solution
View More Questions