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Find the value of expression (cos(pi/2)+...

Find the value of expression `(cos(pi/2)+i sin(pi/2))(cos(pi/(2^2))+i sin(pi/(2^2)))......oo`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a is a complex number such that |a|=1, then find the value of a, s...

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  2. If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=...

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  3. Find the value of expression (cos(pi/2)+i sin(pi/2))(cos(pi/(2^2))+i s...

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  4. If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' a...

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  5. If a ,b are complex numbers and one of the roots of the equation x^2+a...

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  6. If |z1|=|z2|=1, then prove that |z1+z2|= |1/z1+1/z2∣

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  7. For x in (0,1) , prove that i^(2i+3) ln((i^3x^2+2x+i)/(i x^2+2x+i^3))=...

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  8. The sum of the non-real root of (x^2+x-2)(x^2+x-3)=12 is a.-1 b....

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  9. If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1....

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  10. The number of roots of the equation sqrt(x-2)(x^2-4x+3)=0 is (A) Th...

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  11. If z1,z2 and z3,z4 are two pairs of conjugate complex numbers, then ar...

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  12. If x=1+i is a root of the equation x^3-i x+1-i=0, then the other real ...

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  13. Find the modulus, argument, and the principal argument of the complex ...

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  14. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

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  15. If the expression x^2+2(a+b+c)x+3(b c+ca+a b) is a perfect square, the...

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  16. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4 and a...

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  17. The curve y=(lambda+1)x^2+2 intersects the curve y=lambdax+3 in exactl...

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  18. if z and w are two non-zero complex numbers such that absz=absw and ar...

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  19. The number of irrational roots of the equation (4x)/(x^2+x+3)+(5x)/(x...

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  20. If |z+barz|+|z-barz|=2 then z lies on (a) a straight line (b) a se...

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