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State true or false for the following. ...

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` .

A

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

B

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

C

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

D

none of these

Text Solution

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The correct Answer is:
b
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
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  2. The general value of the real angle θ, which satisfies the equation, (...

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  3. State true or false for the following. If z is a complex number such...

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  4. If z + z^(-1)= 1, then find the value of z^(100) + z^(-100).

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  5. Let A,B and C represent the complex number z1, z2, z3 respectively on ...

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  6. Find the number of solutions of the equation z^(2)+|z|^(2)=0.

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  7. The number of solutions of the equation z^(2) + barz =0 is .

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  8. The centre of a square is at the origin and one of the vertex is 1-i e...

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  9. Let za n domega be two complex numbers such that |z|lt=1,|omega|lt=1a ...

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  10. The system of equation |z+1+i|=sqrt2 and |z|=3}, (where i=sqrt-1) ha...

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  11. The triangle with vertices at the point z1z2,(1-i)z1+i z2 is

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  12. Let a and b two fixed non-zero complex numbers and z is a variable com...

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  13. The centre of a square ABCD is at z=0, A is z(1). Then, the centroid o...

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  14. If z=x+i y , then the equation |(2z-i)/(z+1)|=m does not represents a ...

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  15. If x^2-2xcos theta+1=0, then the value of x^(2n)-2x^n cosntheta+1, n ...

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  16. If p^(2)-p+1=0, then the value of p^(3n) can be

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  17. The complex number 2^(n)/(1 + i)^(2n) + (1+i)^(2n)/2^(n), n in I is e...

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  18. If arg (z(1)z(2))=0 and |z(1)|=|z(2)|=1, then

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  19. If i = sqrt(-1), omega is non-real cube root of unity then ((1 + i)^(2...

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  20. If z is a complex number satisfying z+z^(-1) =1 " then " z^(n) + z...

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