Find the locus of the complex number z=x+iy satisfying relations arg(z-1)=pi/4 and |z-2-3i|=2 . Illustrate this on the argand plane.

Question

aravindg · Answer

Do you know what  |z-2-3i|=2 represent?

anonymous · Answer

if you solve this,it will represent a circle.

aravindg · Answer

Correct! And can you find the center?

anonymous · Answer

yeah ofcourse ! but then there are two different conditions :(

aravindg · Answer

No problem.. We can solve it first analyse each case then lets pt it together.

anonymous · Answer

the first one is y = x-1

aravindg · Answer

Great

anonymous · Answer

can you put both the results together and tell me the answer ?

aravindg · Answer

Lets do it together and try to reach the final answer. The purpose of Openstudy is just that!

anonymous · Answer

that would be great

aravindg · Answer

Good so we have analysed both condition. Now to put it together call the locus point as (h,k) ie h+ik

anonymous · Answer

yeah okay

aravindg · Answer

Now h+ik satisfies both these conditions:

k=h-1 ------------(1)
|(h-2)+i(k-3)|=2----(2)

Put 1 in 2 and solve.

anonymous · Answer

thank you so much :)

aravindg · Answer

You are welcome :) Just always remember to first break down the question into small parts then join it together. Good luck!