For any z- the value of -1- z -1- z - n -1- z -1- z - n is equal toA- 2 B -1-2C- 1D- 4

Since 1 + z and 1 + z̅ are conjugates of each other, there fore | 1+z| = | 1+z̅| Hence, | 1+z/1+ z̅|^n= | 1+z|^n/| 1+ z̅|^n=1 Similarly | 1+z̅/1+ z|^n= | 1+z̅|^ ...

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Byju's Answer

Standard XII

Mathematics

Condition for Coplanarity of Four Points

For any z, th...

Question

For any z, the value of ${∣ ∣ \frac{1 + z}{1 + ¯ z} ∣ ∣}^{n}$ + ${∣ ∣ \frac{1 + ¯ z}{1 + z} ∣ ∣}^{n}$ is equal to

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Solution

The correct option is A 2
Since 1 + z and 1 + $¯ z$ are conjugates of each other, there fore $| 1 + z | = | 1 + ¯ z |$
Hence, ${∣ ∣ \frac{1 + z}{1 + ¯ z} ∣ ∣}^{n} = \frac{{| 1 + z |}^{n}}{{| 1 + ¯ z |}^{n}} = 1$
Similarly ${∣ ∣ \frac{1 + ¯ z}{1 + z} ∣ ∣}^{n} = \frac{{| 1 + ¯ z |}^{n}}{{| 1 + z |}^{n}} = 1$

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For any z, the value of ∣∣1+z1+ ¯z ∣∣n + ∣∣1+¯z 1+ z∣∣n is equal to

The correct option is A 2Since 1 + z and 1 + ¯z are conjugates of each other, there fore |1+z|=|1+¯z | Hence, ∣∣1+z1+¯z∣∣n=|1+z|n|1+¯z|n=1 Similarly ∣∣1+¯z1+z∣∣n=|1+¯z|n|1+z|n=1

For any z, the value of ${∣ ∣ \frac{1 + z}{1 + ¯ z} ∣ ∣}^{n}$ + ${∣ ∣ \frac{1 + ¯ z}{1 + z} ∣ ∣}^{n}$ is equal to