# Complex number- Locus and finding the greatest, lowest of argument

• Aug 21st 2006, 04:10 AM
kingkaisai2
Complex number- Locus and finding the greatest, lowest of argument
I have no idea what a locus means so
The complex number u is given by u=(7+4i)/(3-2i). In the form x+yi, x=i, y=2

Sketch and argand diagram showing the point representing the complex number u. Show on the same diagram the locus of the complex number z such that [z-u]=2. Give a thorough description would be good.

Find the greatest value of argument. Urgent.
• Aug 21st 2006, 06:11 AM
CaptainBlack
Quote:

Originally Posted by kingkaisai2
I have no idea what a locus means so
The complex number u is given by u=(7+4i)/(3-2i). In the form x+yi, x=i, y=2

Should have $x=1,\ y=2$ for the above.

Quote:

Sketch and argand diagram showing the point representing the complex number u.
You should be able to do the above now.

Quote:

Show on the same diagram the locus of the complex number z such that [z-u]=2. Give a thorough description would be good.
I presume that this last should be $|z-u|=2$, which is a circle
of radius $2$ centred at $u$.

Quote:

Find the greatest value of argument.
This is now just a bit of geometry (look like $135^{\circ}$ or $3 \pi/4 \mbox{ radians}$
to me, but I haven't checked in detail)

RonL