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Cramer's Rule

if |z1|=1, |z...

Question

if |z1|=1, |z2|=1, |1/z1+1/z2|=3/2, then find 2|z1+z2|

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z_{1} = 2 - i, z_{2} = 1 + i

∣ ∣ ∣ \frac{z_{1} + z_{2} + 1}{z_{1} - z_{2} + 1} ∣ ∣ ∣

z_{1} = 2 - i, z_{2} = 1 + i

∣ ∣ ∣ \frac{z_{1} + z_{2} + 1}{z_{1} - z_{2} + i} ∣ ∣ ∣

| z_{1} - 1 | < 2, | z_{2} - 2 | < 1

| z_{1} + z_{2} |

z_{1} \neq - z_{2}

| z_{1} + z_{2} | = ∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} ∣ ∣ ∣

| z_{1} - 1 | < 1, | z_{2} - 2 | < 2, | z_{3} - 3 | < 3,

| z_{1} + z_{2} + z_{3} |

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