# Complex Numbers: Argand Diagrams

• May 2nd 2009, 09:48 AM
Fibonacci
Complex Numbers: Argand Diagrams
determine the cartesian form and hence sketch the locus of z
Re(z)= l z l

given that l z-1+i l ≤ 1 find
a) the minimun and maximun value for l z l
b) the minimun and maximun value for arg (z)

given that l z-1+i l ≤ 2 and Re (z) ≥ 1 find
a) min and max value for l z l
b) min and maz value for arg (z)

thank you...
• May 2nd 2009, 03:42 PM
mr fantastic
Quote:

Originally Posted by Fibonacci
determine the cartesian form and hence sketch the locus of z
Re(z)= l z l

Mr F says: Let z = x + iy. Post your work if you're still stuck.

given that l z-1+i l ≤ 1 find

Mr F says: Do you realise the boundary of this region is a circle with centre at z = 1 - i and radius 1?

a) the minimun and maximun value for l z l
b) the minimun and maximun value for arg (z)

Mr F says: Draw a line from z = 0 that passess through z = 1 - i. You can now use geometrical properties, Pythagoras' Theorem and trigonometry of right-triangles to get these answers.

given that l z-1+i l ≤ 2 and Re (z) ≥ 1 find
a) min and max value for l z l
b) min and maz value for arg (z)

Mr F says: Consider what I've said above.

thank you...

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