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Given that for any complex number z, abs...

Given that for any complex number z, `absz^2 = zoverlinez` . Prove that `abs(z_1+z_2)^2 + abs(z_1-z_2)^2 = 2[abs(z_1)^2 + abs(z_2)^2]` where `z_1` and `z_2` are any two complex numbers.

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V PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Find the real numbers x and y if (x-iy)(3+5i) is the conjugate of - 6 ...

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  2. Find the modulus of (1+i)/(1-i) - (1-i)/(1+i)

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  3. If (x+iy)^3 = u + iv, then show that u/x+v/y=4(x^2-y^2)

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  4. If alpha and beta are different complex numbers with absbeta = 1, then...

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  5. Find the number of non zero integral solutions of the equation abs(1-i...

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  6. If (a+ib) (c+id) (e+if) (g+ih) = A+iB, then show that (a^2+b^2) (c^2+d...

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  7. If ((1+i)/(1-i))^m = 1 then find the least integral value of m

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  8. Show that a real value of 'x' will satisfy the equation (1- ix )/(1+i...

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  9. Find the modulus of the following complex numbers i) 1+i tan alpha i...

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  10. Show that the images of the given complex numbers 3+2 i , 5 i,-3+2 ian...

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  11. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

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  12. Which of the following is true? i) a)|(z)1+(z)(2)| le|(z)(1)|+|(z)(2)|...

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  13. Represent the complex number z=1+i in the polar form.

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  14. If (5+6 i)/(3+4 i)=x+i y, then find the value of x-y.

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  15. If a+ib=(x+i)^2/(2x^2+1), prove that a^2+b^2=(x^2+1)^2/(2x^2+1)^2

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  16. If z(1)and z(2) are non -zero complex numbers, then show that (z(1) z(...

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  17. If |z+i|=abs(z- i), find z

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  18. Find the conjugate of (1)/(3+4 i)

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  19. Convert the following complex numbers into polar form -1 -i

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  20. Solve the quadratic equation 2 x^(2)-4 x+3=0 by using the general expr...

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