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Sum of Infinite Terms

on 7: If z=x+...

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on 7: If z=x+ iy, then find the value of arg \vert z\rbrack.

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z = x + i y

(z + 2)

=

(z + i)

, then? find relation between real and imaginary part of z.

Q. The value of

∣ ∣ \sqrt{{a r g z + a r g (- ¯ z) - 2 π} {a r g (- z) + a r g (¯ z)}} ∣ ∣

(\forall x + i y, i = \sqrt{-} 1, x, y > 0)

z = x + i y

(\frac{z - 2}{z + 2}) = \frac{π}{6}

then the locus of z is

z = x + i y

| z + 1 | = | z - 1 |

a r g (\frac{z - 1}{z + 1}) = \frac{π}{4}

z \neq 0

log z = log | z | + i (a r g z)

- π < a r g (z) \leq π

a r g (z)

stands for the principal argument of

z

z log (e^{x + i y})

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