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If the ratio (z-i)/(z-1) is purely imagi...

If the ratio `(z-i)/(z-1)` is purely imaginary, prove that the point z lies on the circle whose centre is the point `(1)/(2) (1+i)` and radius is `(1)/(sqrt2)`

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ICSE-COMPLEX NUMBERS-Chapter Test
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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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  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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  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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