If z(1)+z(2) are two complex number and ...

If `z_(1)+z_(2)` are two complex number and `|(barz_(1)-2bar z_(2))/(2-z_(1)barz_(2))|=1, |z_(1)| ne `, then show that `|z_(1)|=2`.

Promotional Banner

Promotional Banner

Topper's Solved these Questions

MISCELLANEOUS EXAMPLES
CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)|124 Videos
MISCELLANEOUS EXAMPLES
CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos
MISCELLANEOUS EXAMPLES
CHHAYA PUBLICATION|Exercise TRIGONOMETRY|148 Videos
METHOD OF SUBSTITUTION
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos
ORDER AND DEGREE OF DIFFERENTIAL EQUATION
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

If z_(1),z_(2) are two complex numbers , prove that , |z_(1)+z_(2)|le|z_(1)|+|z_(2)|

If z_(1) , z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 and iz_(1)=Kz_(2) , where K in R , then the angle between z_(1)-z_(2) and z_(1)+z_(2) is

If z_(1)and z_(2) are conjugate complex number, then z_(1)+z_(2) will be

If z_1 and z_2 be two complex numbers such that abs((z_1-2z_2)/(2-z_1barz_2))=1 and abs(z_2) ne1 , what is the value of abs(z_1) ?

If z_(1)and z_(2) be any two non-zero complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then prove that, arg z_(1)=arg z_(2) .

If |z_(1)|=|z_(2)|=1 and argz_(1)+argz_(2)=0 then show that z_(1)=1

If z_1 and z_2 be two complex numbers show that Re(barz_1z_2)=1/2(z_1barz_2+barz_1z_2) where Re(z) is the real part if z .

If z_(1),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|Z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 , then find |z_(1)+z_(2)+z_(3)| .

If z_(1) , z_(2) are complex numbers such that Re(z_(1))=|z_(1)-2| , Re(z_(2))=|z_(2)-2| and arg(z_(1)-z_(2))=pi//3 , then Im(z_(1)+z_(2))=

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=- bar z _2dot

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA

Show that (a+ omega +omega ^(2))(a+omega ^(2)+omega ^(4))(a+omega ^(4)...
Text Solution
|
Let z and omega tow complex number. If |z|= |omega| and areg (z) +arg...
Text Solution
|
If z(1)+z(2) are two complex number and |(barz(1)-2bar z(2))/(2-z(1)ba...
Text Solution
|
If x+iy moves on the line 3x+4y+5=0, prove that the minimum value of ...
Text Solution
|
If |z^(2)|=9|z|, find the maximum and minimum values of |z|.
Text Solution
|
Find the greatest value of |z| when |z-(6)/(z)|=2,z being a complex nu...
Text Solution
|
Find the least value of |z+(1)/(z)| if |z| ge 3 (z being a complex ...
Text Solution
|
If the roots of the equation ix^(2)-(b^(2)+c^(2))x+(c^(2)+d^(2))^(2)=0...
Text Solution
|
If one root of the equation ax^(2)-2ibx-ic=0 be square of the other, t...
Text Solution
|
Solve (7y^(2)+1)/(y^(2)-1)-4 ((y^(2)-1)/(7y^(2)+1))=-3
Text Solution
|
Solve (x-(x)/(x+1))^(2)+2x((x)/(x+1))=3
Text Solution
|
If alpha and beta are the roots of ax^(2)+bx+cid=0 find the equation ...
Text Solution
|
Show that, 3^(n)-(n)/(1!)3^(n-1)+(n(n-1))/(2!)3^(n-2)-...+(-1)^(n)="...
Text Solution
|
Find the coefficient of x^(-5) in ""^(n)C(0)-""^(n)C(1) ((2x-1)/(x)...
Text Solution
|
Find the degree of theexpansion, {x+(x^(3)-1)^(1//2)}^(5)+{x-(x^(3)-...
Text Solution
|
Find the term independent of x in the expansion, ((x+1)/(x^(2//3)-x^(...
Text Solution
|
Find the remainder if number 2^(2003) is divided by 17.
Text Solution
|
Find last three digits of the number 17^(256).
Text Solution
|
Find the sum of the series, (1^(2))/(3)+(1^(2)+2^(2))/(5)+(1^(2)+2^(...
Text Solution
|
Find the value of sum(r=1)^(n) (r)/(1+r^(2)+r^(4))
Text Solution
|