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If z=3/(2+costheta+isintheta) then show ...

If `z=3/(2+costheta+isintheta)` then show that z lies on a circle in the complex plane

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If z be complex no. and (z-1)/(z+1) be purely imaginary show that z lies on the circle whose centre is at origin and the radius is 1

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z=((1+isqrt3)^2)/(4i(1-isqrt3)) is a complex number then a. arg(...

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  2. If alpha,beta,gamma are such that alpha+beta+gamma=2,""alpha^2+beta^2+...

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  3. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

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  4. If z=x +i y such that |z+1|=|z-1| and arg((z-1)/(z+1))=pi/4 , then fin...

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  5. If x y=2(x+y),xlt=y and x ,y in N , then the number of solutions of t...

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  6. If I m((z-1)/(e^(thetai))+(e^(thetai))/(z-1))=0 , then find the locus ...

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  7. If pa n dq are distinct prime numbers, then the number of distinct im...

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  8. The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. ...

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  9. What is locus of z if |z-1-sin^(-1)(1/sqrt3)|+|z+cos^(-1)(1/sqrt3)-p...

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  10. If abs(z-2-i)=abszabssin(pi/4-argz) then locus of z is

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  11. The number of integral values of a for which the quadratic equation (x...

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  12. Ifomega is the imaginary cube root of unity and a+b+c=0 then show that...

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  13. If z is a complex number having least absolute value and |z-2+2i|=1,th...

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  14. If the equation cot^4x-2cos e c^2x+a^2=0 has at least one solution, th...

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  15. Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/...

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  16. If omega is the imaginary cube root of 1 then prove that (a+bomega+com...

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  17. The number of the real solutions of the equation x^2-3absx+2=0 is

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  18. If |z-1| + |z + 3| le 8, then prove that z lies on the circle.

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  19. If z1a n dz2 are the complex roots of the equation (x-3)^3+1=0,t h e n...

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  20. If the quadratic equation a x^2+b x+6=0 does not have real roots and b...

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