Advertisements
Advertisements
प्रश्न
Show that the equation `z^3 + 2bar(z)` = 0 has five solutions
उत्तर
Given `z^3 + 2bar(z)` = 0
z3 = `-2 bar(z)`
|z3| = `|- 2| |bar(z)|`
|z|3 = 2|z| .......`[because |"z"| = |bar("z")|]`
|z|3 – 2|z| = 0
|z| [|z|2 – 2] = 0
|z| = 0|z|2 = 2
`"z"bar(z)` = 2
z = `2/bar(z) = +- sqrt(2)` ......`[because bar(z) = (- z^3)/2]`
z = `2/((z^3/-2)`
z4 = 4
It has 4 non zero solutions.
∴ Including z = 0 we have 5 solutions.
APPEARS IN
संबंधित प्रश्न
Find the modulus of the following complex numbers
`(2"i")/(3 + 4"i")`
Find the modulus of the following complex numbers
`(2 - "i")/(1 + "i") + (1 - 2"i")/(1 - "i")`
For any two complex numbers z1 and z2, such that |z1| = |z2| = 1 and z1 z2 ≠ -1, then show that `(z_1 + z_2)/(1 + z_1 z_2)` is real number
Which one of the points 10 – 8i, 11 + 6i is closest to 1 + i
If |z| = 3, show that 7 ≤ |z + 6 – 8i| ≤ 13
If |z| = 2 show that the 8 ≤ |z + 6 + 8i| ≤ 12
If z1, z2 and z3 are three complex numbers such that |z1| = 1, |z2| = 2, |z3| = 3 and |z1 + z2 + z3| = 1, show that |9z1z2 + 4z1z3 + z2z3| = 6
Find the square roots of 4 + 3i
Choose the correct alternative:
If = `((sqrt(3) + "i")^3 (3"i" + 4)^2)/(8 + 6"i")^2`, then |z| is equal to
Choose the correct alternative:
If |z – 2 + i| ≤ 2, then the greatest value of |z| is
Choose the correct alternative:
If (1 + i)(1 + 2i)(1 + 3i) ……. (l + ni) = x + iy, then 2.5.10 …… (1 + n2) is
Choose the correct alternative:
The value of `((1 + sqrt(3)"i")/(1 - sqrt(3)"i"))^10` is
The square roots of -18i are ______
If α and β are roots of the equation x2 + 5|x| – 6 = 0, then the value of |tan–1α – tan–1 β| is ______.
