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Prove that : (i) sqrt(i)= (1+i)/(sqrt(...

Prove that : (i) `sqrt(i)= (1+i)/(sqrt(2))` (ii) `sqrt(-i)=(1- i)/(sqrt(2))` (iii) `sqrt(i)+sqrt(-i)=sqrt(2)`

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NAGEEN PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATION -EXERCISE 5B
  1. Prove that ((-1+isqrt(3))/(2))^(3) is a positive integer.

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  2. Convert [(3+2i)/( 3-2i)+ (3 -2i)/(3+2i)] in the form of (a+ib).

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  3. Prove that : (i) sqrt(i)= (1+i)/(sqrt(2)) (ii) sqrt(-i)=(1- i)/(sqr...

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  4. Find the sum and product of the complex number (3-4i) with its conjug...

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  5. Find the sum and product of the complex number (-1 +2i) with its conj...

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  6. Find the multiplicative inverse of the following complex number: (2+sq...

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  7. Write the following in the form of ordered pair : (i) 3-2i (ii)...

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  8. Convert the following in the form of a complex number : (i) (2, -5)...

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  9. Find the values of x and y from the following : (i) (3x -7)+2iy=-5y+...

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  10. If z=1+2i, show that z^(2)-2z+5=0. Hence find the value of z^(3) +7z^...

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  11. Z=-5+4i then Z^4 +9Z^3 +35Z^2 – Z + 4 =

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  12. If z(1)=2-i, z(2)=1+ 2i, then find the value of the following : (i)...

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  13. If x + i y =(a+i b)/(a-i b),prove that x^2+y^2=1.

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  14. (x+iy)^(1/3) =(a+ib) then prove that (x/a+y/b)=4(a^2-b^2)

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  15. If = (a^(2) + 1)^(2)/(2a-i)=x+iy," then when is the value of " x^(2)+...

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  16. Write the least positive integral value of n for which ((1+i)/(1-i))^n...

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  17. The complex number z is purely imaginary , if

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  18. If a^2+b^2=1.Then (1+b+ia)/(1+b-ia)=

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  19. Find the real values of theta for which the complex number (1+i costhe...

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  20. Find the square root of the following : (i) 3-4i (ii) 4+6isqrt(5) ...

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