If |z(1)|=|z(2)|andamp(z(1))+amp(z(2))=0...

If `|z_(1)|=|z_(2)|andamp(z_(1))+amp(z_(2))=0,` then

`z_(1) = -z_(2)`

`z_(1) = overline(z)_(2) `

`z_(1)z_(2) = 1`

None of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise LEVEL - 2|50 Videos
COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos
COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos
CIRCLES
VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos
CONIC SECTIONS
VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find the of z_(1)z_(2).

If |z_(1)|=|z_(2)| and arg (z_(1))+"arg"(z_(2))=0 , then

Consider z_(1)andz_(2) are two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| Statement -1 amp (z_(1))-amp(z_(2))=0 Statement -2 The complex numbers z_(1) and z_(2) are collinear. Check for the above statements.

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_(1)+z_(2)|^(2) = |z_(1)|^(2) +|z_(2)|^(2) " the " 6/pi amp (z_(1)/z_(2)) is equal to ……

Show that if z_(1)z_(2)+z_(3)z_(4)=0 and z_(1)+z_(2)=0 ,then the complex numbers z_(1),z_(2),z_(3),z_(4) are concyclic.

State true or false for the following. Let z_(1) " and " z_(2) be two complex numbers such that |z_(2) + z_(2)| = |z_(1) | + |z_(2)| , then arg (z_(1) - z_(2)) = 0

If arg (z_(1)z_(2))=0 and |z_(1)|=|z_(2)|=1 , then

Prove that traingle by complex numbers z_(1),z_(2) and z_(3) is equilateral if |z_(1)|=|z_(2)| = |z_(3)| and z_(1) + z_(2) + z_(3)=0

If z_(1) and z_(2) are to complex numbers such that two |z_(1)|=|z_(2)|+|z_(1)-z_(2)| , then arg (z_(1))-"arg"(z_(2))

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 1

(1+2i+3i^2)/(1-2i+3i^2) equals i b. -i c. -1 d. 4
Text Solution
|
If sqrt(3)+i=(a+i b)//(c+i d) , then find the value of tan^(-1)(b//a)t...
Text Solution
|
If |z(1)|=|z(2)|andamp(z(1))+amp(z(2))=0, then
Text Solution
|
If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6...
Text Solution
|
If omega(!= 1) be an imaginary cube root of unity and (1+omega^2)^n=(...
Text Solution
|
Prove that x^(3p) + x^(3q+1) + x^(3r+2) is exactly divisible by x^2+x+...
Text Solution
|
If z= x + yi and omega = ((1- zi))/(z-i), then |omega|=1 implies that ...
Text Solution
|
The locus of z which satisfies the inequality log (0.3) abs(z-1) gt l...
Text Solution
|
The set of points in an Argand diagram which satisfy both abs(z)le4 an...
Text Solution
|
If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...
Text Solution
|
For x(1), x(2), y(1), y(2) in R if 0 lt x(1)lt x(2)lt y(1) = y(2)...
Text Solution
|
If alpha,betaandgamma are the cube roots of P(p)lt0), then for any x, ...
Text Solution
|
If z(1) , z(2), z(3) are three complex numbers in A.P., then they lie ...
Text Solution
|
If the cube roots of unity are 1,omega,omega^2, then the roots of the ...
Text Solution
|
about to only mathematics
Text Solution
|
If Re ((z + 2i)/(z+4))= 0 then z lies on a circle with centre :
Text Solution
|
If z is a complex number satisfying the relation |z+ 1|=z+2(1+i), then...
Text Solution
|
The number of solutions of z^3+ z =0 is (a) 2 (b) 3 (c) 4 (d) 5
Text Solution
|
If z= costheta+isintheta , then the value of (z^(2n)-1)/(z^(2n)+1) ...
Text Solution
|
If f(x)=x^(4)-8x^(3)+4x^(2) +39 and f(3+2i)=a+ib then a:b equals
Text Solution
|