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If |z-i R e(z)|=|z-I m(z)| , then prove ...

If `|z-i R e(z)|=|z-I m(z)|` , then prove that `z` , lies on the bisectors of the quadrants.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Match the statements in column-I with those I column-II [Note: Here z ...

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  2. If x ,y in R satify the equation x^2+y^2-4x-2y+5=0, then the value of...

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  3. If |z-i R e(z)|=|z-I m(z)| , then prove that z , lies on the bisectors...

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  4. For any integer k , let alphak=cos((kpi)/7)+isin((kpi)/7),w h e r e i...

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  5. If x=1+1/(3+1/(2+1/(3+1/(2)))) a 52/2 b. 55/71 c. 60/52 d. 71/55

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  6. Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot

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  7. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

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  8. Find the values of a for which all the roots of the euation x^4-4x^3-8...

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  9. If z is any complex number satisfying |z-3-2i|lt=2 then the maximum va...

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  10. Let |(( bar z 1)-2( bar z 2))//(2-z1( bar z 2))|=1 and |z2|!=1,where z...

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  11. If x=2+2^(2//3)+2^(1//3) , then the value of x^3-6x^2+6x is (a)3 b...

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  12. Let 1,w,w^2 be the cube root of unity. The least possible degree of a ...

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  13. If z1a n dz2 are complex numbers and u=sqrt(z1z2) , then prove that |z...

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  14. The least value of the expression x^2+4y^2+3z^2-2x-12 y-6z+14 is a...

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  15. If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 ...

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  16. If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus o...

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  17. If x=2+2^(2//3)+2^(1//3) , then the value of x^3-6x^2+6x is

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  18. Let z=x+i ydot Then find the locus of P(z) such that (1+ bar z )/z ...

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  19. (costheta + isintheta)^4/(sintheta + icostheta)^5 is equal to.

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  20. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

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