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Prove that: x^4=4=(x+1+i)(x+1-i)(x-1+i(x...

Prove that: `x^4=4=(x+1+i)(x+1-i)(x-1+i(x-1-i)dot)`

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CBSE COMPLEMENTARY MATERIAL-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -Short Answer Type Questions
  1. Solve the following equations by using the general expression for a qu...

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  2. Find the square root of 7-30Sqrt(-2)

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  3. Prove that: x^4=4=(x+1+i)(x+1-i)(x-1+i(x-1-i)dot)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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