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If x+iy=3/(2+costheta +i sin theta), the...

If `x+iy=3/(2+costheta +i sin theta)`, then show that `x^2+y^2=4x-3`

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3

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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE LEVEL 1
  1. If 8iotaz^3+12z^2-18z+27iota=0 then: a. |z|=3/2 b. |z|=2/3 c. |z|=...

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  2. If a complex number z lies in the interior or on the boundary of a cir...

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  3. If x+iy=3/(2+costheta +i sin theta), then show that x^2+y^2=4x-3

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  4. Suppose z(1), z(2), z(3) represent the vertices A, B and C respectivel...

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  5. Suppose that three points z(1), z(2), z(3) are connected by the relati...

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  6. If the number (z-1)/(z+1) is purely imaginary, then

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  7. If z s a complex number such that -pi/2 leq arg z leq pi/2, then which...

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  8. If |omega|=1, then the set of points z=omega+1/omega is contained in o...

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  9. The number of complex numbers z such that |z|=1a n d|z// z + z //z=1...

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  10. If |z1|=|z2|=|z3|=1 are twu complex numbers such that |z1|=|z2|=sqrt2...

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  11. Let z(1), z(2), z(3) be three non-zero complex numbers such that z(1) ...

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  12. If |z1|=|z2|=|z3|=1 then value of |z1-z3|^2+|z3-z1|^2+|z1-z2|^2 cannot...

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  13. Let z1z2,z3, be three complex number such that z1+z2+z3=0 and |...

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  14. Let z(1), z(2), z(3) be three complex numbers such that |z(1)| = |z(2)...

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  15. Suppose z is a complex number such that z ne -1, |z| = 1, and arg(z) =...

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  16. Let a = Im((1+z^(2))/(2iz)), where z is any non-zero complex number. T...

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  17. Number of complex numbers such that |z| = 1 and z = 1 - 2 bar(z) is

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  18. Let z(1), z(2) be two complex numbers such that z(1) ne 0 and z(2)//z(...

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  19. If z = i(1+sqrt(3)),"then"z^(4)+2z^(3)+4z^(2) + 5 is equal to

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  20. If the fourth roots of unity are z1, z2, z3, z4 and z1^2+z2^2+z3^2+z4^...

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