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If (x+i y)^3=u+i v , then show that u/x...

If `(x+i y)^3=u+i v ,` then show that `u/x+v/y=4(x^2-y^2)`

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0\ ,...

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  2. If x ,y and z are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2x ...

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

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  4. Let a >0,b >0 and c >0 . Then, both the roots of the equation a x^2+b ...

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  5. If the sum of square of roots of the equation x^2+(p+i q)x+3i=0 is 8, ...

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  6. Column I, Column II y=(x^2-2x+4)/(x^2+2x+4),x in R ,t h e ny c a n...

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  7. If sqrt(x+i y)=+-(a+i b), then findsqrt( x-i ydot)

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  8. Match the following for the equation x^2+a|x1=0,w h e r ea is a parame...

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  9. Find the ordered pair (x ,y) for which x^2-y^2-i(2x+y)=2idot

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  10. If a ,b ,c are non zero complex numbers of equal modlus and satisfy a ...

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  11. Column I, Column II If a ,b ,c ,a n dd are four zero real number...

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  12. Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then...

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  13. Let a is a real number satisfying a^3+1/(a^3)=18 . Then the value of a...

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  14. Find non zero integral solutions of |1-i|^x=2^xdot

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  15. If (1+i)(1+2i)(1+3i)......(1+n i)=(x+i y) , show that 2. 5. 10...... (...

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  16. If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c<0 , then wh...

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  17. If omega is a cube root of unity, then find the value of the following...

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  18. If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the values of...

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  19. If omega is a cube root of unity, then find the value of the following...

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  20. Find the domain and range of f(x)=sqrt(x^2-4x+6)

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