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If z = x+iy, prove that arg(z -1) = tan^...

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

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A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. If two points P and Q are represented by the complex numbers z1 and z2...

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

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

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

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

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

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

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  8. Express 1 + i in modulus amplitude form

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

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

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

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

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

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

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  15. Express (1+i)/sqrt3+i in the form x + iy. Hence, find the polar form o...

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  16. Nisha derived the polar form of (1+i)/sqrt3+i by using the polar forms...

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  17. Using the polar form and x + iy form of (1+i)/sqrt3+i, prove that cosp...

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  18. Fill in the blank by choosing the correct answer from the bracket. If ...

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  19. Suppose alpha and beta are two complex numbers so that absbeta = 1. Ra...

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  20. Match the following

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