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If complex number `z(z!=2)` satisfies the equation `z^2=4z+|z|^2+(16)/(|z|^3)` ,then the value of `|z|^4` is______.

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Verified by Experts

The correct Answer is:
4
We know that
`|z + iomega| le |z| +|iomega| =|z| +|i| |omega|=1`
Given `|z+iomgea| = 2 rArr|z| =|omega| =1`.
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CENGAGE-COMPLEX NUMBERS-Exercise (Numerical)
  1. Modulus of nonzero complex number z satifying barz + z =0 and |z|^(2)-...

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  2. If the expression (1 + ir)^3 is of the form of s(1+ i) for some real '...

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  3. If complex number z(z!=2) satisfies the equation z^2=4z+|z|^2+(16)/(|z...

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  4. The complex number z satisfies z+|z|=2+8i. find the value of |z|-8

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  5. Let |z|=2a n dw-(z+1)/(z-1),w h e r ez ,w , in C (where C is the set ...

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  6. If z is a complex number satisfying z^4+z^3+2z^2+z+1=0 then the set of...

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  7. Let 1, omega,omega^(2) be the cube roots of unity. The least possib...

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  8. If omega is the imaginary cube roots of unity, then the number of p...

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  9. Suppose that z is a complex number the satisfies |z-2-2i|lt=1. The max...

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  10. If |z+2-i|=5 and maxium value of |3z +9-7i| is M, then the value of M ...

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  11. Let Z1 = (8 + i)sin theta + (7 + 4i)cos theta and Z2 = (1 + 8i)sin th...

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  12. Let A={a in R} the equation (1+2i)x^3-2(3+i)x^2+(5-4i)x+a^2=0 has at ...

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  13. Find the minimum value of the expression E= |z|^2+ |z-3|^2 + |z- 6i|^2...

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  14. If z1 lies on |z-3| + |z + 3| = 8 such that arg z1 = pi//6 , ...

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  15. If z satisfies the condition arg(z + i) = (pi)/(4) . Then the ...

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  16. Let omega ne 1 be a complex cube root of unity. If ( 4 + ...

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  17. Let z be a non - real complex number which satisfies the equatio...

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  18. If z, z 1 and z2 are complex numbers such that z = z 1 z2 ...

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  19. Let z1 , z 2 and z3 be three complex numbers such that z1 + z2+ ...

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  20. Let alpha be the non-real 5 th root of unity. If z1 and z2...

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