Consider two complex number and satisfying and

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Consider two complex number

z

and

w

satisfying

|z|=1

and

|w-2| + |w-4| = 2

. Then which of the following statement(s) is/are correct? (A)

\operatorname{Re}(zw)

can never exceed 4. (B) If

\arg(z) = \arg(w)

, then

|z+2|

is equal to 3. (C) The minimum value of

|z-w|

is equal to 2. (D) The minimum value of

|z-w|

is equal to 6.