If 0 < arg (z) < π,
Question:

If 0 < arg (z) < π, then arg (z) – arg (–z) = ____________.

Solution:

For 0 < arg z < π

Let z = r(cosθi sinθ)

i.e arg z = θ

Then –z = – r(cosθ + i sinθ)

$=-r(+\cos \theta+i(+\sin \theta))$

$=(-1) r e^{i \theta}$

$=e^{i \pi} r e^{i \theta}$

$=r e^{i(\theta+\pi)}$

i.e arg (–z) = θ + π

⇒ arg z – arg(–z) = θ – θ – π

= – π

Administrator

Leave a comment

Please enter comment.
Please enter your name.