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If z= x + yi and |2z + 1| = |z- 2i|, sho...

If `z= x + yi and |2z + 1| = |z- 2i|`, show that `3(x^(2) + y^(2)) + 4(x-y)=3`

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ICSE-COMPLEX NUMBERS-Chapter Test
  1. If z(1), z(2) in C (set of complex numbers), prove that |z(1) + z(2)| ...

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  2. If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1, find the locus of ...

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  3. Simplify: (1- 3omega + omega^(2)) (1 + omega- 3omega^(2))

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  4. Find the locus of z satisfying |(z-3)/(z+1)|=3 in the complex plane.

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  5. Given that (2 sqrt3 cos 30^(@) - 2i sin 30^(@))/(sqrt2 (cos 45^(@) + i...

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  6. Simplify : (1- omega) (1- omega^(2)) (1- omega^(4)) (1- omega^(8))

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  7. Find the locus of a complex number z= x + yi, satisfying the relation ...

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  8. Find the real values of x and y satisfying the equality (x-2 + (y-3)i)...

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  9. If i= (sqrt-1), prove that following (x+1+i) (x+ 1-i) (x-1-i) (x-1+ i)...

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  10. If z= x + yi and |2z + 1| = |z- 2i|, show that 3(x^(2) + y^(2)) + 4(x-...

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  11. Find the amplitude of the complex number "sin" (6pi)/(5) + i (1- "cos"...

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  12. Express (1- 2i)/(2+i) + (3+i)/(2-i) in the form a + bi

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  13. Find the value of x and y given that (x + yi) (2-3i)=4+i

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  14. If the ratio (z-i)/(z-1) is purely imaginary, prove that the point z l...

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  15. If (-2 + sqrt-3) (-3 + 2 sqrt-3) = a + bi, find the real numbers a and...

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  16. If 1, omega, omega^(2) are the three cube roots of unity, then simplif...

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  17. Find the locus of a complex number z= x+yi, satisfying the relation |3...

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  18. Find the modulus and argument of the complex number (2 + i)/(4i + (1+ ...

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  19. If |z-3+ i|=4, then the locus of z is

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  20. The locus of the point z is the Argand plane for which |z +1|^(2) + |z...

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