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Express (1-i)/(sqrt3+i) in polar form...

Express `(1-i)/(sqrt3+i)` in polar form

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Verified by Experts

The correct Answer is:
`(1)/sqrt2[cos((-5pi)/12) + isin((-5pi)/12)]`
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A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Convert the following complex numbers into polar form 1 - i

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  2. Represent the complex number sqrt3+i in the polar form.

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  3. Express (1-i)/(sqrt3+i) in polar form

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  4. Express (1-i)(sqrt3+i) in polar form

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  5. Plot the points represented by the complex numbers 1+i, 2+i, 2+3i, 1+3...

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  6. What are the cartesian co-ordinates of the points 1+i, 2+i, 2+3i, 1+3...

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  7. If two points P and Q are represented by the complex numbers z1 and z2...

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  8. If the points P,Q,R,S are representing the complex numbers -1, 3i, 3+2...

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  9. If z = x+iy, prove that arg(z -1) = tan^(-1)(y/(x-1)) and arg(z+1) = t...

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  10. If arg((z-1)/(z+1)) = pi/2, show that x^2+y^2-1=0

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  11. Express sqrt3-i in polar form using the polar form of sqrt3+i

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  12. Use De-Moivere's theorem to find (sqrt3-i)^9 and (sqrt3-i)^(-1) in rec...

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  13. Determine also, for which values of nepsilonZ, (sqrt3-i)^n is real

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  14. Express 1 + i in modulus amplitude form

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  15. Prove that (1 + i)^4 = -4

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  16. Represent the complex number 1+sqrt3i in the polar form.

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  17. What is the polar form of 1 - sqrt3i?

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  18. Prove that (1 + sqrt3i)^n + (1 - sqrt3i)^n = 2^(n+1) cos ((npi)/3) for...

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  19. Solve : x^2 - 2x + 4 = 0

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  20. If alpha and beta are the roots of x^2 - 2x + 4 = 0, Prove that alpha^...

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