perplexus.info :: Just Math : Maximizing Complex Ratios

Maximizing Complex Ratios (Posted on 2024-06-14)

If z is a complex number such that |z|=3, then find the maximum value of the expression |z-i|/|z+1|.

No Solution Yet Submitted by Danish Ahmed Khan

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computer solution

| Comment 1 of 3

mx=0;

for theta=0:.00000005:2*pi

a=3*cos(theta); b=3*sin(theta);

r=norm([a,b-1])/norm([a+1,b]);

if r>mx

mx=r;

mxa=a; mxb=b;

end

disp([mxa mxb])

mx =

1.66225322815709

Column 1

-2.82093725734824

Column 2

-1.02093730958594

The maximum is approximately 1.66225322815709, at

z = -2.82093725734824 - 1.02093730958594 i

Edited on June 14, 2024, 9:36 am

Posted by Charlie on 2024-06-14 09:35:05

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