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Given z is a complex number with modulus...

Given `z` is a complex number with modulus 1. Then the equation `[(1+i a)//(1-i a)]^4=z` has all roots real and distinct two real and two imaginary three roots two imaginary one root real and three imaginary

A

all roots, real and distinct

B

two real and two imaginary

C

three roots real and one imaginary

D

one root real and three imaginary

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a
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. If n is a positive integer greater than unity z is a complex number sa...

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  2. If at least one value of the complex number z=x+iy satisfies the condi...

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  3. Given z is a complex number with modulus 1. Then the equation [(1+i a)...

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  4. The center of a regular polygon of n sides is located at the point z=0...

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  5. If the points z(1),z(2),z(3) are the vertices of an equilateral triang...

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

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  7. The inequality |z-4| < |z-2| represents

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  8. Number of non-zero integral solution of the equation |1-i| ^(n)=2^(n),...

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  9. If "Im"(2z+1)/(iz+1)=-2, then locus of z, is

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  10. lf z(!=-1) is a complex number such that [z-1]/[z+1] is purely imagina...

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  11. If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

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  12. If z(1),z(2), z(3) are vertices of an equilateral triangle with z(0) i...

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  13. If z1,z2 are two complex numbers such that Im(z1+z2)=0,Im(z1z2)=0, the...

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  14. If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight ...

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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. Let g(x) and h(x) are two polynomials such that the polynomial P(x) =g...

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  17. If g(x) and h(x) are two polynomials such that the polynomials P(x)=g(...

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  18. If |z(1)|=|z(2)|=|z(3)| and z(1)+z(2)+z(3)=0, then z(1),z(2),z(3) are ...

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  19. If x(n)=cos(pi/3^(n))+isin((pi)/(3^(n))), then x(1),x(2),x(3),……………….....

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  20. If (a1+ib1)(a2+ib2).....(an+ibn)=A+iB, then (a1^2+b1^2)(a2^2+b2^2).......

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