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Let z be a complex number satisfying the...

Let `z` be a complex number satisfying the equation `z^3-(3+i)z+m+2i=0,w h e r em in Rdot` Suppose the equation has a real root. Then root non-real root.

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MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
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  2. The quadratic equation z^2 +(p+ip')z+q+iq' =0 where p,p',q,q' are all ...

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  3. Let z be a complex number satisfying the equation z^3-(3+i)z+m+2i=0,w ...

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  5. The real values of the parameter 'a' for which at least one complex nu...

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  6. If |z1|=|z2|=dot=|zn|=1, prove that |z1+z2+z3++zn|=1/(z1)+1/(z2)+1/(z3...

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

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

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

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

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

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

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

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

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

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