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If x+iy=(a+ib)/(a-ib), then prove that x...

If `x+iy=(a+ib)/(a-ib)`, then prove that `x^2+y^2=1`

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JBD PUBLICATION-MODEL PAPER (10)-EXERCISE
  1. If sinx=-5/13 and x lies in IIIrd quadrant. Find the value of secx+tan...

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  2. Prove that: 2 sin^2(3pi)/4+2cos^2pi/4+2s e c^2pi/3=10

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  3. If x+iy=(a+ib)/(a-ib), then prove that x^2+y^2=1

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  4. Find (a+b)^4-(a-b)^4. Hence evaluate : (sqrt3 +sqrt2)^4 -(sqrt3 -sqrt...

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  5. Find the rth term from the end in the expansion of (x+a)^n.

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  6. Show that the points A(2,3,4), B(3,4,2), C(4,2,3) form the vertices o...

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  7. Identify the quantifier in the following statements and write the nega...

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  8. Find the component statements of the following and check whether it is...

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  9. Let A, B, and C be the sets such that A uu B = A uu C and A nn B = A n...

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  10. If f (x) = loge ((1+x)/(1-x)), prove that: f (x) +f (y)= f ((x+y)/(1+x...

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  11. Prove the following by using the principle of mathematical induction f...

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  12. If ""^(n)C(r ): ""^(n)C(r+1)=1:2 and ""^(n)C(r+1): ""^(n)C(r+2)=2:3, ...

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  13. Find the number of different signals that can be generated by arrangin...

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  14. Find the sum of all natural numbers lying between 100 and 1000, which ...

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  15. Find the three number is G.P. such that their sum is 19 and sum of the...

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  16. P(a,b) is the mid-point of a line segment between axes. Show that the ...

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  17. Find the equations of the ellipse whose length of the major axis is 20...

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  18. Evaluate: underset(xrarr5)lim (1-sqrt(x-4))/5.

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  19. If siny = xsin(a+y), prove that dy/dx=sin^2(a+y)/sina

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  20. An integer is chosen from the first 200 integers. Find the probability...

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