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

1. ## 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.

2. 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.

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

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 $u$.

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

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### least and greatest value of an argument of a conplex number

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