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Logarithm of a Complex Number

If z1 = 1 + 3...

Question

If z₁ = 1 + 3i and z₂ = 2 + i, then $Re (\frac{{¯ z}_{2} z_{1}}{z_{2}})$ is

यदि z₁ = 1 + 3i तथा z₂ = 2 + i है, तब $Re (\frac{{¯ z}_{2} z_{1}}{z_{2}})$ का मान है

A

3

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B

–3

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C

2

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D

–2

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Solution

The correct option is A 3
Solution

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Q. For any two complex numbers

z_{1}

z_{2}

| z_{1} | \neq | z_{2} |

{∣ ∣ \sqrt{2} z_{1} + i \sqrt{3}_{2} ∣ ∣}^{2} + {∣ ∣ \sqrt{3}_{1} + i \sqrt{2} z_{2} ∣ ∣}^{2}

z_{1} = 1 + \sqrt{3} i

z_{2} = 1 - \sqrt{3} i,

\frac{z_{1}^{100} + z_{2}^{100}}{z_{1} + z_{2}} =

z_{1} = (2 - i)

z_{2} = (1 + i),

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

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

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

z_{1} = (2 - i)

z_{2} = (1 + i),

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

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