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Show that the complex number z, satisfyi...

Show that the complex number z, satisfying the condition arg `((z -1)/(z + 1))=(pi)/(4) lies on a circle.

A

`(sqrt(2)+1)+0i`

B

`0+(sqrt(2)+1)i`

C

`0+(sqrt(2)-1)i`

D

`(-sqrt(2)+1)+0i`

Text Solution

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The correct Answer is:
b
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Chapter Test
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  2. The area of the triangle (in square units) whose vertices are i, omega...

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  3. Show that the complex number z, satisfying the condition arg ((z -1)/(...

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  4. If A,B,C are three points in the Argand plane representing the complex...

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  5. If z(bar(z+alpha))+barz(z+alpha)=0, where alpha is a complex constant,...

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  6. Let A,B,C be three collinear points which are such that AB.AC=1 and th...

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  7. z1, z2, z3,z4 are distinct complex numbers representing the vertices o...

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  8. If z be a complex number, then |z-3-4i|^(2)+|z+4+2i|^(2)=k represent...

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  9. In Argand diagram, O, P, Q represent the origin, z and z+ iz respectiv...

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  10. If (2z(1))/(3z(2)) is purely imaginary number, then |(z(1)-z(2))/(z(1)...

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  11. If omega is a cube root of unity then find the value of sin((omega^(10...

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  12. If center of a regular hexagon is at the origin and one of the vertice...

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  13. if the roots of the equation z^(2) + ( p +iq) z + r + is =0 are real ...

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  14. Q. Let z1, z2, z3 be three vertices of an equilateral triangle circums...

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  15. If omega is the complex cube root of unity, then the value of omega+om...

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  16. The locus of z =I +2exp(i(theta + pi/4)) , ( where theta is parameter...

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  17. If z lies on the circle |z-1|=1, then (z-2)/z is

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  18. If a gt 0 and the equation |z-a^(2)|+|z-2a|=3, represents an ellipse, ...

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  19. For any complex number z , find the minimum value of |z|+|z-2i|dot

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  20. Find the greatest and the least value of |z1+z2| ifz1=24+7ia n d|z2|=6...

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