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If alpha & beta are any two complex numb...

If `alpha & beta` are any two complex numbers, prove that
`|alpha+beta|^2+|alpha-beta|^2=2(|alpha|^2+|beta|^2)`

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MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
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  2. If |z1|=|z2|=dot=|zn|=1, prove that |z1+z2+z3++zn|=1/(z1)+1/(z2)+1/(z3...

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  3. If alpha & beta are any two complex numbers, prove that |alpha+beta|...

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  4. Prove that |alpha+sqrt(alpha^2-beta^2)|+|alpha-sqrt(alpha^2-beta^2)|= ...

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  5. Prove the identity,|1-z1barz2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2)

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  6. Among the complex numbers z satisfying the condition |z+3-sqrt(3)i|=sq...

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  7. Given, z=cos.(2pi)/(2n+1)+i sin.(2pi)/(2n+1), 'n' a positive integer ...

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  8. If alpha=e^(i2pi//7)a n df(x)=a0+sum(k-0)^(20)ak x^k , then prove that...

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  9. Let alpha+ibeta,alpha, beta epsilon R, be a root of the equation x^(3)...

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  10. If A,B and C are angle of a triangle of a triangle ,the value of |{:(...

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  11. If n is a positive integer, prove the following (1+cos theta+i sin the...

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  12. If n is a positive integer, show that (1 + i)^(n) + (1 - i)^(n)...

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  13. Find all those roots of the equation z^12 – 56z^6 – 512 = 0 whose ima...

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  14. Let a complex number alpha,alpha!=1, be a rootof hte euation z^(p+q)-z...

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  15. Solve (z-1)^4-16=0 . Find sum of roots. Locate roots, sum of roots and...

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  16. If omega is a non-real cube root of unity, then the value of (1-omega...

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  17. If omega is an imaginary cube root of unity then prove that If omeg...

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  18. If omega is a cube root of unity, prove that (1+omega-omega^2)^3-(1...

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  19. If omega is a cube root of unity, prove that (a+bomega+comega^2)/(c+...

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  20. If omega is a cube root of unity, then find the value of the following...

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