The number of solutions of equation - z - z -1- z -2- z -3-4 and z z - z - z -5-4 where z is a complex number -A- 0B- 2C- 1D- Infinite

The correct option is A 0z z̅ z z̅ = 5/4 z = x + iy ⇒ x^2 + y^2 2x 5/4 = 0.....(i) |z| + |z – 1| + |z – 2| + |z – 3| = 4 ....(ii) ∵ |z| + |z 1| + |z ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Conjugate of a Complex Number

The number of...

Question

The number of solutions of equation $| z | + | z - 1 | + | z - 2 | + | z - 3 | = 4 a n d z ¯ z - z - ¯ z = \frac{5}{4}$ where z is a complex number ?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Infinite

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

$z ¯ z - z - ¯ z = \frac{5}{4} z = x + i y$
$\Rightarrow x^{2} + y^{2} - 2 x - \frac{5}{4} = 0$ .....(i)
$| z | + | z - 1 | + | z - 2 | + | z - 3 | = 4$ ....(ii)
$∵ | z | + | z - 1 | + | z - 2 | + | z - 3 | \geq 4$
$∴$ No solution

Suggest Corrections

Similar questions

Q. If complex number

z (z \neq 2)

satisfies the equation

z^{2} = 4 z + {| z |}^{2} + \frac{1}{{| z |}^{3}}

, then the value of

{| z |}^{- 4}

For all complex numbers $z_{1}, z_{2}$ satisfying $| z_{1} | = 12$ and $| z_{2} - 3 - 4 i | = 5$ , the minimum value of $| z_{1} - z_{2} |$ is

Q. Numbers of solutions of the equation

z^{3} + \frac{3 (¯ ¯ ¯ z)^{2}}{| z |} = 0

where

z

is a complex number is

Q. If

z

is a complex number and

α = \frac{z + i}{i z + 2}

, where

i = \sqrt{- 1}

. Suppose

α

is a real number then

Q. Number of solutions of the equation

z^{3} + [3 \frac{{¯ ¯ ¯ z}^{2}}{| z |}] = 0

where,

z

is a complex number is

Join BYJU'S Learning Program

The number of solutions of equation |z|+|z−1|+|z−2|+|z−3|=4 and z¯z−z−¯z=54 where z is a complex number ?

z¯z−z−¯z=54z= x+iy ⇒x2+y2−2x−54=0.....(i) |z|+|z–1|+|z–2|+|z–3|=4 ....(ii) ∵|z|+|z−1|+|z−2|+|z−3|≥4 ∴ No solution

The number of solutions of equation $| z | + | z - 1 | + | z - 2 | + | z - 3 | = 4 a n d z ¯ z - z - ¯ z = \frac{5}{4}$ where z is a complex number ?

$z ¯ z - z - ¯ z = \frac{5}{4} z = x + i y$
$\Rightarrow x^{2} + y^{2} - 2 x - \frac{5}{4} = 0$ .....(i)
$| z | + | z - 1 | + | z - 2 | + | z - 3 | = 4$ ....(ii)
$∵ | z | + | z - 1 | + | z - 2 | + | z - 3 | \geq 4$
$∴$ No solution