Home
Class 11
MATHS
If (1+i)z = (1-i)barz, "then show that ...

`If (1+i)z = (1-i)barz, "then show that "z = -ibarz.`

Text Solution

Verified by Experts

We have, `(1+i)z = (1-i)barz rArr barz = (barz)/(barz)=(1-i)/(1+i).`
`rArr (z)/(barz)=(1-i)/(1+i)(1-i)/(1-i) rArr (z)/(barz)=(1+i^(2)-2i)/(1-i^(2)) " " [:.i^(2)=-1] `
`rArr (z)/(barz)=(1-1-2i)/(2) rArr (z)/(barz)=i`
`rArr z = - i barz " "Hence proved. `
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise LONG ANSWER TYPE QUESTIONS|14 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise TRUE/FALSE|9 Videos

  • BINOMIAL THEOREM

    NCERT EXEMPLAR|Exercise True/False|7 Videos

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Objective type|13 Videos

Similar Questions

Explore conceptually related problems

If (1+i)z=(1-i)bar(z) then z is

If (1+i)z=(1-i)phi z, then show that z=-iz

Knowledge Check

  • If ((1+i) z= (1-i))bar(z), then

    A
    z lies on a straight line
    B
    for all such `z ne 0, "arg" (z) = 3pi//4`
    C
    all such z are given by `z=t (1-i), t in R`
    D
    z must be purely real

  • If (1+i)z=(1-i)barz , then z is equal to

    A
    `t(1-i), t in R`
    B
    `t(1+i),t in R`
    C
    `t/(1+i),t in R^(+)`
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    if (1+i)z=(1-i)bar(z) then z is

    If z=ibarz then

    z_(1) "the"z_(2) "are two complex numbers such that" |z_(1)| = |z_(2)| . "and" arg (z_(1)) + arg (z_(2) = pi," then show that "z_(1) = - barz_(2).

    If z = x + iy where i = sqrt(-1) , then what does the equation zbarz +|z|^2 +4(z+barz)-48=0 represent?

    If the real part of (barz +2)/(barz-1) is 4, then show that the locus of the point representing z in the complex plane is a circle.

    Solve for z: z^2 = (ibarz)^2 .

    Home
    Profile