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Let a=i^i and consider the following st...

Let `a=i^i` and consider the following statements `S_1: a=e^(-pi/2)`, `S_2`:The value of `sin(In a)-1`, `Im(a)+arg(a)=0` Now identify the correct combination of the true statements.

A

`S_(1),S_(2)` only

B

`S_(1),S_(3)` only

C

`S_(1),S_(2),S_(3)`

D

`S_(1)` only

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
  1. Which of the following is not true ?

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  2. The complex number z1,z2 and z3 satisfying (z1 - z3)/(z2 - z3) = ( 1 -...

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  3. Let a=i^i and consider the following statements S1: a=e^(-pi/2), S2:T...

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  4. If z^(2)+z+1=0 then the value of (z+1/z)^(2)+(z^(2)+1/z^(2))^(2)+(z...

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  5. If omega is an imaginary fifth root of unity, then find the value of l...

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  6. If 1,alpha1,alpha2,alpha3,.........,alpha(3n) be the roots of the equt...

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  7. If z(1),z(2),z(3),z(4) are two pairs of conjugate complex numbers, th...

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  8. If |z-4 +3i| le 2 then the least and the greatest values of |z| are q

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  9. If |z1|=2,|z2|=3,|z3|=4 and |2z1+3z2+4z3|=4 then the expression |8z2z3...

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  10. If z1 = cos theta + i sin theta and 1,z1,(z1)^2,(z1)^3,.....,(z1)^(n-1...

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  11. The area of the triangle whose vertices are represented by the complex...

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  12. The maximum value of |z| where z satisfies the condition |z+(2/z)|=2 i...

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  13. The value of (1-tan^2 15^@)/(1+tan^2 15^@) is

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  14. both roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are

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  15. If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2, then the locus of z is

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  16. If arg z = pi/4 ,then

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  17. The z^2 + z|z| + |z|^2 = 0, then locus of Z is

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  18. The least value of p for which the two curves argz=pi/6 and |z-2sqrt(...

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  19. Re((z+4)/(2z-1)) = 1/2, then z is represented by a point lying on

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  20. If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(...

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