Question

if mod(z)=max{mod(z-1), mod(z+1)} then:

(a) mod(z+z)=1/2

(b) z+z=1

(c) mod(z+z(conjugate))=1

(d) N.O.T

Answer 1

Correct answer is (c)

Explanation:

|z|=max{|z−1|,|z+1|}

Let z=a+ib, where a and b are real numbers

So, |z|=max{|a+ib−1|,|a+ib+1|}

|z| = max{sqrt{(a - 1)^2 + b^2}, sqrt{(a + 1)^2 + b^2}}