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Dividing f(z) by z- i, we obtain the re...

Dividing `f(z)` by `z- i`, we obtain the remainder i and dividing it by `z + i`, we get the remainder 1 + i, then remainder upon the division of `f(z)` by `z^2+1` is

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Suppose a ,b ,c in I such that the greatest common divisor for x^2+a ...

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  2. Find the value of following expression: [(1-cospi/(10)+isinpi/(10))/(1...

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  3. Dividing f(z) by z- i, we obtain the remainder i and dividing it by z...

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  4. If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consec...

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  5. If z1, z2 in C ,z1^2+z2^2 in R ,z1(z1^2-3z2^2)=2 and z2(3z1^2-z2^2)...

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  6. If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamm...

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  7. If x+y+z=12 andx^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then find the valu...

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  8. Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4), where n is a pos...

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  9. The set {R e((2i z)/(1-z^2)): z is a complex number , |z|=1,z=+-1} is...

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  10. If the equation x^2+ax+bc=0" and " x^2+bx+ca=0 have a common root, the...

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  11. If a r g["z"1("z"3-"z"2)]=a r g["z"3("z"2-"z"1)] , then prove that O ,...

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  12. If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2...

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  13. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) , then c is equ...

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  14. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

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  15. If z=(a+ib)^5+(b+ia)^5 then prove that Re(z)=Im(z), where a,b in R.

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  16. If a and b are positive numbers and eah of the equations x^2+a x+2b=0 ...

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  17. Find the real values of x and y for which the following equation is sa...

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  18. The three angular points of a triangle are given by Z=alpha, Z=beta,Z=...

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  19. Suppose a ,b ,c are the roots of the cubic x^3-x^2-2=0. Then the value...

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  20. It is given that n is an odd integer greater than 3 but n is not a mul...

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