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`(1+i)^(n_1)+(1+i^3)^(n_1)+(1+i^5)^(n_2)+(1+i^7)^(n_2)` is a real number if

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let z and omega be two complex numbers such that |z|lt=1,|omega|lt=1 ...

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  2. Consider the equation x^2+2x-n=0 where n in N and n in [5,100] The t...

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  3. (1+i)^(n1)+(1+i^3)^(n1)+(1+i^5)^(n2)+(1+i^7)^(n2) is a real number if

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  4. The total number of values a so that x^2-x-a=0 has integral roots, wh...

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  5. If i=sqrt(-1) then 4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365 is ...

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  6. Let P(x)=x^3-8x^2+c x-d be a polynomial with real coefficients and wi...

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  7. If a r g(z)<0, then a r g(-z)-"arg"(z) equals pi (b) -pi (d) -pi/2 ...

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  8. Let P(x)=5/3-6x-9x^2a n dQ(y)=-4y^2+4y+(13)/2dot if there exists uniq...

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  9. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

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  10. if a lt c lt b, then check the nature of roots of the equation (a ...

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  11. Let z1 and z2 be the nth roots of unity which subtend a right angle at...

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  12. If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+...

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  13. The complex numbers z1,z2 and z3 satisfying (z1-z3)/(z2-z3)=(1-isqrt3)...

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  14. The value of a so that the sum of the squares of the roots of the equa...

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  15. For all complex niumbers z1, z2 satisfying absz1=12 and abs(z2-3-4i)=5...

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  16. If x1, a n dx2 are the roots of x^2+(sintheta-1)x-1/2(cos^2theta)=0, ...

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  17. If y="sec"(tan^(-1)x),t h e n(dy)/(dx)a tx=1 is (a)cos(pi/4) (b) s...

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  18. If p ,q in {1,2,3,4,} , then find the number of equations of form px^2...

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  19. If a^2+b^2=1 t h e n (1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+...

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  20. Find the domain and the range of f(x)=sqrt(x^2-3x.)

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