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For any two complex numbers z(1) and z(2...

For any two complex numbers `z_(1) and z_(2)` and any real numbers a and b, prove that `|az_(1)-bz_(2)|^(2) + |bz_(1) + az_(2)|^(2) = (a^(2) + b^(2)) [|z_(1)|^(2) + |z_(2)|^(2)]`

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ICSE-COMPLEX NUMBERS-Chapter Test
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  4. Express (13i)/(2-3i) in the form A + Bi

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

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  6. If omega and omega^(2) are cube roots of unity, prove that (2- omega +...

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  7. If z(1), z(2) in C (set of complex numbers), prove that |z(1) + z(2)| ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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