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Let z be a complex number satisfying equ...

Let `z` be a complex number satisfying equation `z^p-z^(-q),w h e r ep ,q in N ,t h e n` if `p=q` , then number of solutions of equation will be infinite. if `p=q` , then number of solutions of equation will be finite. if `p!=q` , then number of solutions of equation will be `p+q+1.` if `p!=q` , then number of solutions of equation will be `p+qdot`

A

if p=q, then number of solution of equation will infinte.

B

if p=q, then number of solutions of equaiton will finite

C

if `pne q`, then number of solutions of equaiton will `p+q+1`.

D

if `p ne q`, then number of solutions of equaiton will be `p+q`

Text Solution

Verified by Experts

The correct Answer is:
A, B
If q=p, then equation becomes `z^(p)= z^(-q)` and it has infinte
number of solutions because any z `in ` R will satisfly it. `p ne q`,
let `p gt q`, then `z^(p) = z^(-q)`
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CENGAGE-COMPLEX NUMBERS-Exercise (Multiple)
  1. System of equaitons |z+3|-|z-3| = 6 and |z-4|=r where r in R^(+) has

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  2. Let the equaiton of a ray be |z-2|-|z-1-i| = sqrt(2). If the is stri...

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  3. Given that the two curves a r g(z)=pi/6a n d|z-2sqrt(3)i|=r intersect ...

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  4. On the Argand plane ,let z(1) = - 2+ 3z,z(2)= - 2-3z and |z| = 1. T...

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  5. Let S = { z: x = x+ iy, y ge 0,|z-z(0)| le 1}, where |z(0)|= |z(0) - o...

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  6. If P andn Q are represented by the complex numbers z(1) and z(2) such...

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  7. Loucus of complex number satifying are arg[(z-5+4i)//(z+3-2i)] = - pi...

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  8. Equation of tangent drawn to circle |z| = r at the point A(z0), is

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  9. If n is a natural number gt 2, such that z^(n) = (z+1)^(n), then

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  10. If |z-(1//z)=1,t h e n (|z|)(m a x)=(1+sqrt(5))/2 b. (|z|)(m in)=(sqr...

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  11. If 1,z(1),z(2),z(3),…….,z(n-1) be the nth roots of unity and omega b...

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  12. Let z be a complex number satisfying equation z^p-z^(-q),w h e r ep ,q...

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  13. Which of the following is ture ?

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  14. If from a point P representing the complex number z1 on the curve |z...

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  15. A complex number z is rotated in anticlockwise direction by an angle ...

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  16. z(1),z(2),z(3) and z(1),z(2),z(3) are nonzero complex numbers such th...

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  17. Given z=f(x)+ig(x)w h e r ef,g:(0,1)vec(0,1) are real valued functions...

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  18. Let a, b, c be distinct complex numbers with |a|=|b|=|c|=1 and z(1), z...

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  19. If a,b,c,d in R and all the three roots of az^3 + bz^2 + cZ + d=0 ha...

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  20. If (3)/(2+e^(itheta)) =ax + iby, then the locous of P(x,y) will repre...

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