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If z ne 0 be a complex number and "arg"(...

If `z ne 0` be a complex number and `"arg"(z)=pi//4`, then

A

`"Re"(z)="Im"(z)` only

B

`Re(z) = Im(z) gt 0`

C

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

D

none of these

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b
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
  1. If omega(!=1) is a cube root of unity, then value of the determinant|1...

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  2. Let z and omega be two non-zero complex numbers, such that |z|=|omega|...

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  3. If z ne 0 be a complex number and "arg"(z)=pi//4, then

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  4. (1+i)^8+(1-i)^8=?

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  5. What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n...

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  6. If alpha\ a n d\ beta are different complex numbers with |beta|=1,\ fi...

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  7. For any complex number z, the minimum value of |z|+|z-1|, is

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  8. If (3pi)/(2) gt alpha gt 2 pi, find the modulus and argument of (1 -...

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  9. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Arg and plane, the...

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  10. Area of the triangle formed by 3 complex numbers, 1+i,i-1,2i, in the A...

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  11. If omega is a comples cube root of unity, then (1 - omega + omega^(2) ...

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  12. The locus represented by the equation |z-1| = |z-i| is

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  13. If z=i log(2-sqrt(3)) then cosz

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  14. If a=cos alpha+i sin alpha, b=cos beta+isin beta,c=cos gamma+i sin gam...

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  15. lf z1,z2,z3 are vertices of an equilateral triangle inscribed in the c...

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  16. The general value of the real angle θ, which satisfies the equation, (...

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

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

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

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

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