If -z1- - 2- - z2 be the point in which sartisfies the condition z2-z2-iz2-z2 - 8-2- then the minimum value of -z1-z2- is

Iven: |z_1|=2, (z_2+z_2) i(z_2 z_2)=8√(2) |z_1| = 2 ⇒ x^2+y^2 = 4 (z_2+z_2) i(z_2 z_2) = 8√(2) ⇒ x+y = 4√(2) AB = OB r AB = 2 ...

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Equation of Conics in Complex Form

If |z1| = 2, ...

Question

$If | z_{1} | = 2, & z_{2} be the point in which sartisfies$ $the condition (z_{2} +_{2}) - i (z_{2} -_{2}) = 8 \sqrt{2},$ then the minimum value of $| z_{1} - z_{2} |$ is

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z_{1} = 5 + 12 i

| z_{2} | = 4

z_{1}

z_{2}

∣ ∣ ∣ \frac{z_{1} + {i z}_{2}}{z_{1} {i z}_{2}} ∣ ∣ ∣ = 1

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

z_{1} = i z_{2}

z_{1} - z_{3} = i (z_{3} - z_{2})

| z_{3} | = \sqrt{2} | z_{1} |

If arg ( $Z_{1}$ ) = $α$ , arg ( $Z_{2}$ ) = $β$ , the value of $| Z_{1} + Z_{2} |^{2}$ is

| z_{1} | = 1, | z_{2} | = 2

| z_{1} + z_{2} |^{2} + | z_{1} - z_{2} |^{2}

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