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For any complex number z,prove that |Re(...

For any complex number z,prove that `|Re(z)|+|I_m(z)|le\sqrt 2 |z|`

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UNITED BOOK HOUSE-NAVA NALANDA-EXERCISE
  1. In how many of the distinct permutaions of the letters in MISSISIPPI d...

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  2. Solve :x^2-(3sqrt2-2i)x-6sqrt2i=0

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  3. For any complex number z,prove that |Re(z)|+|Im(z)|le\sqrt 2 |z|

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  4. Find the direction in which a straight line must be drawn through the ...

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  5. Find the area of the triangle formed by the lines joingn the vertex of...

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  6. Find the domain of definition of the function f(x)=1/(ln(1-x))+sqrt(x+...

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  7. Prove that (AcupB)^c=A^c capB^c[without venn-diagram]

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  8. Four digit number are formed by using the digits 1,2,3,4 and 5 wihout ...

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  9. Find the mean deviation about the median for the following data:

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  10. For any three sets A, B, C, Prove that A cap(BcupC)=(AcapB)cup (A cap ...

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  11. A+B+C=pi,prove that sin^2(A/2)+sin^2(B/2)+sin^2(C/2)=1-2sin(A/2)sin(B/...

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  12. Solve :tanx+tan(x+pi/3)+tan(x+(2pi)/3)=3

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  13. Using the principle of mathematical induction prove that 3^(2n+1)+2^(n...

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  14. If alpha and beta are different complex numbers with |beta|=1, then fi...

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  15. A question paper contains 12 questions divided into three parts.Parts...

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  16. Prove that the inequations (2x+1)/(7x-1)>5and (x+7)/(x-8)>2have no sol...

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  17. Exhibit graphically the solution region of the following system of 'in...

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  18. Prove that the product of the lengths of the perpendiculars drawn from...

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  19. Find the equation of a circle which touches both the axes and the line...

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  20. The focus of a parabola is (1,5)and its directrix is x+y+2=0.Find the...

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