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For any complex number z prove that |R ...

For any complex number `z` prove that `|R e(z)|+|I m(z)|<=sqrt(2)|z|`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Given z is a complex number with modulus 1. Then the equation [(1+i a)...

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  2. The number of value of k for which [x^2-(k-2)x+k^2]xx""[x^2+k x+(2k-1...

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  3. For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

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  4. The point z1=3+sqrt(3)i and z2=2sqrt(3)+6i are given on a complex plan...

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  5. The total number of integral values of a so that x^2 +ax+a+1=0 has int...

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  6. If w=z/[z-1/(3i)] and |w|=1, then find the locus of z

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  7. Let C1and C2 be two circles with C2 lying inside C1 A circle C lying i...

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  8. The number of positive integral solutions of x^4-y^4=3789108 is a.0 ...

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  9. The region of argand diagram defined by |z-1|+|z+1|<=4 (1) interior o...

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

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  11. If alpha,beta are the roots of x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n...

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  12. If (log)(sqrt(3))((|z|^2-|z|+1)/(2+|z|))>2, then locate the region in ...

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  13. If z=((1+isqrt3)^2)/(4i(1-isqrt3)) is a complex number then a. arg(...

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

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

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

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

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

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

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