A z 1 and B z 2 are the points on the circles - z -1 and - z -3 respectively- then-A- -z1-z2-max-1B- -z1-z2-min-4C- -z1-z2-max-4D- -z1-z2-min-1-

The correct option is C ||z_1| |z_2|| ≤ |z_1 z_2| ≤ |z_1| + |z_2| ...

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Geometrical Representation of Argument and Modulus

A z 1 and B z...

Question

$A (z_{1})$ and $B (z_{2})$ are the points on the circles |z| = 1 and |z| = 3 respectively, then:

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z_{1}, z_{2}

| z | = 3

| z | = 4

z_{1}

| z - 3 | = 2

z_{2}

| z - 1 | + | z + 1 | = 3

| z_{1} - z_{2} |_{m i n} = m

| z_{1} - z_{2} |_{m a x} = M

z_{1}

| z - 3 | = 2

z_{2}

| z - 1 | + | z + 1 | = 3

| z_{1} - z_{2} |_{m i n} = m

| z_{1} - z_{2} |_{m a x} = M

z_{2} = {\bar{z}}_{1}

z_{2} = \frac{1}{z_{1}}

If $| z - z_{1} | + | z + z_{2} |$ = $λ, λ \in R^{+}, z_{1}, z_{2}$ are fixed complex numbers, represents an ellipse, then:

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