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

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

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NAGEEN PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATION -EXERCISE 5B
  1. Find the multiplicative inverse of the following complex number: (2+sq...

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

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

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

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

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

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

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

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

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

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

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  12. The complex number z is purely imaginary , if

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

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

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

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  16. If x+iy=3/(2+costheta +i sin theta), then show that x^2+y^2=4x-3

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  17. The sum and product of two complex numbers are real if and only if the...

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  18. If x= cos alpha+ i sin alpha, y = cos beta+ i sin beta, then prove th...

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

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  20. Evaluate : (4+3sqrt(-20))^(1//2)+(4-3 sqrt(-20))^(1//2)

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