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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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If x-iy= sqrt((a-ib)/(c-id)) , prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d^2) .

If x-iy= sqrt((a-ib)/(c-id)) prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d^2) .

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If y = (sin^-1 x)^2 , then prove that (1 -x)^2 (d^2y)/(dx^2) -x dy/dz =2

If 1 +4 sqrt3i = (a+ ib)^2 , prove that : a^2-b^2=1 and ab=2 sqrt3 .

If y=[tan^-1 x]^2 , then prove that : (x^2 + 1)^2 y_2+2x(x^2+1) y_1 = 2 .

If y=[sin^-1 x]^2 , then prove that : (1 -x^2) y_2-xy_1 - 2 = 0 .

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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. If 1 +4 sqrt3i = (a+ ib)^2, prove that : a^2-b^2=1 and ab=2 sqrt3.

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  2. Show that if a, b,c, d in R, bar((a + ib) (c+ id)) = (a-ib)(c- id).

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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. If (a+i)^2/((2a-i))= p + iq, prove that : p^2+q^2 =(a^2+1)^2 /(4a^2+1)...

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  5. If x-iy= sqrt((a-ib)/(c-id)) prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d^...

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  6. If x-iy= sqrt((a-ib)/(c-id)), prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d...

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  7. If (x + iy)^3 = u + iv, then show that : u/x+v/y=4 (x^2-y^2).

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  8. Define addition and multiplication of two complex numbers z1 and z2. H...

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  9. Define addition and multiplication of two complex numbers z1 and z2. H...

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  10. Define addition and multiplication of two complex numbers z1 and z2. H...

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  11. Define addition and multiplication of two complex numbers z1 and z2. H...

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  12. Find the additive inverse of the complex number : -5 + 7i .

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  13. Find the additive inverse of the complex number : (sqrt6+5i)(sqrt6-1...

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  14. Find the difference of the complex numbers : z1=- 3 + 2i and z2= 13-i...

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  15. Find the multiplicative inverse of the following complex numbers : 4...

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  16. Find the multiplicative inverse of the following complex numbers : 2...

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  17. Find the multiplicative inverse of the following complex numbers : 7...

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  18. Find the multiplicative inverse of the following complex numbers : -...

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  19. Find the multiplicative inverse of the following complex numbers : s...

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  20. Find the multiplicative inverse of the following complex numbers : (...

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