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If x+i y=sqrt((1+i)/(1-i)), prove that x...

If `x+i y=sqrt((1+i)/(1-i))`, prove that `x^2+y^2=1`.

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CBSE COMPLEMENTARY MATERIAL-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -Short Answer Type Questions
  1. If arg(z-1)=arg(z+3i), then find (x-1):y, where z=x+iy.

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  2. If z= x+iy and the amplitude of (z-2-3i) is (pi)/(4). Find the relatio...

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  3. If x+i y=sqrt((1+i)/(1-i)), prove that x^2+y^2=1.

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  4. The real value of theta for which the expression (1+icostheta)/(1-2ic...

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  5. If |(z-5i)/(z+5i)|=1 show that z is a real number

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  6. If xn =cos ((pi)/(2^(n)))+isin((pi)/(2^(n)))Prove that x1 x2…..xoo=-1

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  7. Find the real value of x and y if ((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)...

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  8. If (1+i)(1+2i)(1+3i)(1+n i)=(x+i y) , show tht 2. 5. 10 (1+n^2)=x^2+y^...

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  9. If z=2-3i show that z^2=4z+13=0 and hence find the value of 4z^3-3z^2+...

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  10. If ((1+i)/(1-i))^3-((1-i)/(1+i))^3 =a+ib find a and b

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  11. For complex numbers z1 = 6+3i, z2=3-I find (z1)/(z2)

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  12. If ((2+2i)/(2-2i))^(n)=1 find the least positive integral of n.

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  13. if (x+i y)^(1/3) = a+ib then (x/a) + (y/b) equals to

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  14. Convert the following in polar form, (i)-3sqrt2+3sqrt2i

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  15. Convert the following in polar form, (ii) ((sqrt3 -1)-(sqrt3+1)i)/((2s...

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  16. Convert the following in polar form, (iii)i(1+i)

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  17. Convert the following in polar form, (iv)(5-i)/(2-3i)

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  18. Solve (i) x^(2) -(3sqrt2-2i)x-6sqrt2i=0

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  19. Solve the following equations by using the general expression for a qu...

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

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