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If z1,z2 and z3 are complex numbers such...

If `z_1,z_2 and z_3` are complex numbers such that `|z_1|=|z_2|=|z_3|= |1/z_1+1/z_2+1/z_3|=1, then |z_1+z_2+z_3|` is (A) equal to 1 (B) gt1 (C) gt3 (D) equal to 3

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If z_1,z_2,z_3 are complex numbers such that |z_1|=z_2|=|z_3|=|z_1+z_2+z_3|=1, then (1/z_1+1/z_2+1/z_3| is (A) equal to 1 (B) les than (C) greater than 3 (D) equal to 3

If z_(1),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 then |z_(1)+z_(2)+z_(3)| is equal to

Let z_1,z_2,z_3 be three complex numbers such that |z_1|=1,|z_2|=2,|z_3|=3 and |z_1+z_2+z_3|=1. Find |9z_1z_2+4z_1z_3+z_2z_3| .

If |z_1=1,|z_2|=2,|z_3|=3 and |z_1+z_2+z_3|=1, then |9z_1z_2+4z_3z_1+z_2z_3| is equal to (A) 3 (B) 36 (C) 216 (D) 1296

If |z_1|=1, |z_2|=2, |z_3|=3 and |9z_1z_2 + 4z_1z_3 + z_2z_3|=36 , then |z_1+z_2+z_3| is equal to :

If z_1,z_2,z_3 are complex number , such that |z_1|=2, |z_2|=3, |z_3|=4 , the maximum value |z_1-z_2|^(2) + |z_2-z_3|^2 + |z_3-z_1|^2 is :

If z_(1),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=1|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 Then find the value of |z_(1)+z_(2)+z_(3)| is :

CBSE COMPLEMENTARY MATERIAL-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -Short Answer Type Questions
  1. Prove that: x^4=4=(x+1+i)(x+1-i)(x-1+i(x-1-i)dot)

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  2. Show that |(z -2)/(z - 3)| = 2 represents a circle, find its centre ...

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  3. Find all non zero complex numbers z satisfying barz=iz^2

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  4. If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2...

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  5. If z1,z2 are complex numbers such that, (2z1)/(3z2) is purely imaginar...

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  6. If z1 and z2 are complex numbers such that, |1-bar z1z2|^(2)-|z1-z(2^(...

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  7. Find the number of solutions of z^2+|z|^2=0.

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  8. If z1,z2 are complex numbers such that, |(z1-3z2)/(3-z1.bar z2)|=1 and...

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  9. Evaluate x^(4) -4x^(3)+4x^(2)+8x+44, when x=3+2i

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  10. Complex number z1 and z2 satisfy z+barz=2|z-1| and arg (z1-z2) = pi/4 ...

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  11. Solve the following quadratic equation: \ 2x^2-(3+7i)x+(9i-3)=0

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  12. What is the locus of z , if amplitude of (z-2-3i) is pi/2?

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  13. If z=x+i ya n dw=(1-i z)/(z-i) , show that |w|=1 z is purely real.

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  14. Express the following complex numbers in the form r(costheta+isintheta...

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  15. Express the complex number in the form r(cos theta+isin theta) (ii)1-s...

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  16. If (1+i)/(1+2^2i)xx(1+3^2i)/(1+4^2i)xx.......xx(1+(2n-1)^2i)/(1+(2n)^2...

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  17. Find real values of xa n dy for which the complex numbers -3+i x^2ya n...

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  18. The complex numbers z1 z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sqr...

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  19. If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is (|z|)/2 (b) |z| ...

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  20. If z1,z2 and z3 are complex numbers such that |z1|=|z2|=|z3|= |1/z1+1/...

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