# complex numbersWatch

This discussion is closed.
#1
the roots of an equation are 1+2i, 1-2i, -1+2i, -1-2i
represent these on an argand diagram
the root z1 is such that 0<arg z<pi/2
find the maximum value of |z| such that |z-z1|<=2

i have noooooooo idea

thanks alot
0
13 years ago
#2
z1 = 1 + 2i

To maximise |z| subject to |z - (1 + 2i)| <= 2, start at (1 + 2i) and move two units, away from the origin, on the line through 0 and (1 + 2i). Then |z| = |1 + 2i| + 2 = sqrt(5) + 2.
0
#3
thanks
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