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If 1 +4 sqrt3i = (a+ ib)^2, prove that :...

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

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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. Find the values of x and y if : (x+iy)(1+i)=1-i where i=sqrt(-1)

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  2. Find the values of x and y if : ((1+i)x-2i)/(3+i)+((2-3i)y +i)/(3-i)...

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

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

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

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  6. 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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  7. 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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  8. 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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  9. If (x + iy)^3 = u + iv, then show that : u/x+v/y=4 (x^2-y^2).

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

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

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

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

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

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

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

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

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

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