If z is a complex numbers such that z ne...

If z is a complex numbers such that `z ne 0` and `"Re"(z)=0`, then

`Re(z^(2)) = 0`

`Im (z^(2)) = 0`

`Re (z^(2)) = Im (z^(2))`

`Im (z^(2)) lt 0`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMPLEX NUMBERS
MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 1|55 Videos
COMPLEX NUMBERS
MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 2|1 Videos
COMPLEX NUMBERS
MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (NUMERICAL ANSWER TYPE QUESTIONS )|22 Videos
CIRCLES AND SYSTEMS OF CIRCLES
MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|17 Videos
DEFINITE INTEGRALS
MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

Similar Questions

Explore conceptually related problems

State true or false for the following. If z is a complex number such that z ne 0 " and Re " (z)= 0 " then Im" (z^(2)) = 0 .

State ture or false for the following. (i) The order relation is defined on the set of complex numbers. (ii) Multiplication of a non-zero complex number by -i rotates the point about origin through a right angle in the anti-clockwise direction.(iiI) For any complex number z, the minimum value of |z|+|z-1| is 1. (iv) The locus represent by |z-1|= |z-i| is a line perpendicular to the join of the points (1,0) and (0,1) . (v) If z is a complex number such that zne 0" and" Re (z) = 0, then Im (z^(2)) = 0 . (vi) The inequality |z-4|lt |z-2| represents the region given by xgt3. (vii) Let z_(1) "and" z_(2) be two complex numbers such that |z_(1)+z_(2)|= |z_(1)+z_(2)| ,then arg (z_(1)-z_(2))=0 . 2 is not a complex number.

If z is a complex number such that Re(z)=Im(2), then

Suppose z is a complex number such that z ne -1, |z| = 1 and arg(z) = theta . Let w = (z(1-bar(z)))/(bar(z)(1+z)) , then Re(w) is equal to

If z is a purely real complex number such that "Re"(z) lt 0 , then, arg(z) is equal to

Suppose z is a complex number such that z ne -1, |z| = 1, and arg(z) = theta . Let omega = (z(1-bar(z)))/(bar(z)(1+z)) , then Re (omega) is equal to

If z is a complex number such that |z+(1)/(z)|=1 show that Re(z)=0 when |z| is the maximum.

z is a complex number such that |Re(z)| + |Im (z)| = 4 then |z| can't be

MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE

The number of complex numbers satisfying (1 + i)z = i|z|
Text Solution
|
Suppose a, b, c in R and C lt 0. Let z = a + (b + ic)^(2015) + (b-ic)^...
Text Solution
|
The number of solutions of z^(2) + |z| = 0 is
Text Solution
|
The equation |((1+i)z-2)/((1+i)z+4)|=k does not represent a circle whe...
Text Solution
|
If |z| ge 5, then least value of |z - (1)/(z)| is
Text Solution
|
Principal argument of z = (i-1)/(i(1-"cos"(2pi)/(7))+"sin"(2pi)/(7)) i...
Text Solution
|
If (x+iy) = sqrt((a+ib)/(c+id)) then prove that (x^2 + y^2)^2 = (a^2 ...
Text Solution
|
For any three complex numbers z(1),z(2),z(3), if Delta=|{:(1,z(1),bar(...
Text Solution
|
If x, y, a, b in R, a ne 0 and (a + ib) (x + iy) = (a^(2) + b^(2))i, t...
Text Solution
|
If omega (ne 1) is a cube root of unity, then the value of tan[(omega^...
Text Solution
|
If z is purely imaginary and Im (z) lt 0, then arg(i bar(z)) + arg(z) ...
Text Solution
|
The inequality a + ib gt c + id is true when
Text Solution
|
Let z in C be such that Re(z^(2)) = 0, then
Text Solution
|
If z(1),z(2) and z(3),z(4) are two pairs of conjugate complex numbers ...
Text Solution
|
If z = x + iy and 0 le sin^(-1) ((z-4)/(2i)) le (pi)/(2) then
Text Solution
|
If a gt 0 and z|z| + az + 3i = 0, then z is
Text Solution
|
If z is a complex numbers such that z ne 0 and "Re"(z)=0, then
Text Solution
|
If zk=cos((kpi)/10)+isin((kpi)/10), then z1z2z3z4 is equal to
Text Solution
|
If |z(1)| = |z(2)| = 1, z(1)z(2) ne -1 and z = (z(1) + z(2))/(1+z(1)z(...
Text Solution
|
If z in C, then Re(bar(z)^(2))= k^(2), k gt 0, represents
Text Solution
|