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If z=x+iy and x^(2)+y^(2)=16, then the r...

If z=x+iy and `x^(2)+y^(2)=16`, then the range of `abs(abs(x)-abs(y))` is

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alpha is the root (having the least absolute value) of the equation...

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  2. If alpha,beta are roots of x^2-3x+a=0 , a in R and alpha &lt;1< beta...

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  3. If z=x+iy and x^(2)+y^(2)=16, then the range of abs(abs(x)-abs(y)) is

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  4. If a lt b lt c lt d, then for any real non-zero lambda, the quadratic...

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  5. If k>0, |z|=|w|=k, and alpha=(z-bar w)/(k^2+zbar(w)), then Re(alpha) ...

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  6. The quadratic x^2+a x+b+1=0 has roots which are positive integers, th...

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  7. The sum of values of x satisfying the equation (31+8sqrt(15))^(x^2-3)+...

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  8. Let a complex number alpha,alpha!=1, be a rootof hte euation z^(p+q)-z...

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  9. If alpha,beta are real and distinct roots of a x^2+b x-c=0a n dp ,q ar...

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  10. Let a!=0 and p(x) be a polynomial of degree greater than 2. If p(x) le...

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  11. Prove that there exists no complex number z such that |z| &lt; 1/3 an...

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  12. A quadratic equation with integral coefficients has two different prim...

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  13. Find the centre and radius of the circle formed by all the points repr...

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  14. If a ,b ,c are three distinct positive real numbers, the number of rea...

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  15. Find the non-zero complex number z satisfying z =i z^2dot

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  16. Let a,b and c be real numbers such that 4a+2b+c=0 and ab gt 0.Then t...

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  17. If |z|<=1,|w|<=1, then show that |z- w|^2<=(|z|-|w|)^2+(argz-argw)^2

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  18. If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equa...

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  19. For complex numbers z and w, prove that |z|^2w- |w|^2 z = z - w, if...

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  20. If alpha,beta are the roots of the equation a x^2+b x+c=0, then the va...

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