Hi I'm struggling with the following questions where I need to sketch Argand diagrams. I haven't had much exposure to a wide range of these sortsof questions before so I'm not finding the following to be all that easy. There are a couple and some help would be good, thanks.(adsbygoogle = window.adsbygoogle || []).push({});

1. |z| < Argz.

Would this look like a spiral of increasing 'radius.' Like a swirly shape starting at the origin? Would the origin be included? I ask this because I don't think I can have |z| < 0.

Note: -pi < Argz <= pi.

2. log|z| = -2Argz.

Would I just exponentiate both sides to get [tex]\left| z \right| = e^{ - 2Argz} [/tex] ?

If that's correct then what would the shape look like? Perhaps a 'circle' with a a varying radius?

3. [tex]0 < Arg\left( {z - 1 - i} \right) < \frac{\pi }{3}[/tex]

I don't know how to work with this one. The part, z - 1 - i just means the difference between z and (1+i) I think. Let z = x + yi so [tex]0 < Arg\left( {\left( {x - 1} \right) + i\left( {y - 1} \right)} \right) < \frac{\pi }{3}[/tex].

Any help is appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex numbers struggling

**Physics Forums | Science Articles, Homework Help, Discussion**