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If x=cos alpha+i sin alpha and y=cos be...

If `x=cos alpha+i sin alpha` and ` y=cos beta+i sin beta,z=cos gamma+i sin gamma` and if `x+y+z=0` then prove that `(1)/(x)+(1)/(y)+(1)/(z)=0`

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MAHAVEER PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. Find the values of (1+i)^(1/3)

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  2. Find the equation whose roots are the 7^(th)powers of the roots of the...

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  3. If x=cos alpha+i sin alpha and y=cos beta+i sin beta,z=cos gamma+i si...

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  4. If sinalpha+sinbeta+singamma=cosalpha+cosbeta+cosgamma=0then prove tha...

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  5. If sinalpha+sinbeta+singamma=cosalpha+cosbeta+cosgamma=0, then (A) co...

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  6. Express the following in the form of a+ib (2+3i)/(2-i)

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  7. Express the following in the form of a+ib (1+i)/(2+3i)

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  8. Express the following in the form of a+ib (2+i)(2-3i)(4-3i)

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  9. Express the following in the form of a+ib (2+3i)/(5-4i)+(2-3i)/(5+4i)

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  10. Find the conjugate of i/(3+5i)

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  11. Find the conjugate of (2+3i)(3-4i)

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  12. Find the conjugate of (3+i)/(2+5i)

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  13. Find the modulus of (3+4i)/(12+5i)

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  14. Find the modulus and amplitude of the following complex numbers: sqrt3...

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  15. Find the modulus and amplitude of the following complex numbers: -4i

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  16. Find the modulus and amplitude of the following complex numbers: 1+isq...

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  17. Find the modulus and amplitude of the following complex numbers: -1-i

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  18. Find the additive and multiplicative inverse of -4+5i.

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  19. If z1=7+3i and z2=-7+3i then find the following: z1z2

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  20. If z1=7+3i and z2=-7+3i then find the following: barz1barz2

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