>
Exams
>
Mathematics
>
Complex numbers
>
if z geq 3 then the least value of z 4 is
Question:
If \( |z| \geq 3 \), then the least value of \( |z + 4| \) is
Show Hint
In complex numbers, the least value of the sum of distances can be found using the triangle inequality.
VITEEE - 2015
VITEEE
Updated On:
Jan 12, 2026
\( 11/4 \)
\( 11/2 \)
3
4
Show Solution
Verified By Collegedunia
The Correct Option is
A
Solution and Explanation
The least value of \( |z + 4| \) occurs when \( z \) is closest to \( -4 \). Using geometric interpretation, the minimum distance is calculated.
Download Solution in PDF
Was this answer helpful?
0
0
Top VITEEE Mathematics Questions
The product of all values of
$(\cos \alpha + i \sin \alpha)^{3/5}$
is equal to
VITEEE - 2007
Mathematics
Quadratic Equations
View Solution
A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is ___________
$\pi$
cm/s
VITEEE - 2018
Mathematics
Rate of Change of Quantities
View Solution
The interval in which the function
$f\left(x\right) = \frac{4x^{2}+1}{x}$
is decreasing is :
VITEEE - 2018
Mathematics
Rate of Change of Quantities
View Solution
If the normal to the curve
$y = f(x)$
at
$(3,4)$
makes an angle
$\frac{3 \pi}{4}$
with the positive x-axis, then
$f'(3)$
is equal to
VITEEE - 2007
Mathematics
Tangents and Normals
View Solution
The principal value of
$sin^{-1} \left(sin \frac{5\pi}{3}\right)$
is
VITEEE - 2018
Mathematics
Trigonometric Equations
View Solution
View More Questions
Top VITEEE Complex numbers Questions
If $\left|\frac{z-25}{z-1}\right|=5$ , the value of |z|
VITEEE - 2008
Mathematics
Complex numbers
View Solution
If $z$ satisfies the equation $|z|-z=1+2 i$, then $z$ is equal to
VITEEE - 2010
Mathematics
Complex numbers
View Solution
If
$|z| \ge 3$
, then the least value of
$\left|z+\frac{1}{4}\right|$
is
VITEEE - 2015
Mathematics
Complex numbers
View Solution
Amplitude of
$\frac{1+\sqrt{3}i}{\sqrt{3}+1}$
is :
VITEEE - 2018
Mathematics
Complex numbers
View Solution
The value of
$ (1 + \omega - \omega^2)^7$
is
VITEEE - 2016
Mathematics
Complex numbers
View Solution
View More Questions
Top VITEEE Questions
A motor of power
$P_0$
is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe
$n$
times, the power of the motor is increased to
$P_1$
. The ratio of
$P_1 $
to
$P_0$
is
VITEEE - 2009
Power
View Solution
A
$30\,V-90\,W$
lamp is operated on a
$120\,V$
DC line. A resistor is connected in series with the lamp in order to glow it properly. The value of resistance is
VITEEE - 2015
Power
View Solution
Which of the following is not a characteristic of transition elements ?
VITEEE - 2008
properties of d block elements
View Solution
Most crystals show good cleavage because their atoms, ions or molecules are
VITEEE - 2010
Properties of Solids
View Solution
Which of the following sets consists only of essential amino acids ?
VITEEE - 2008
Proteins
View Solution
View More Questions