Let z be an imaginary complex number satisfying - z -1-1- If -2 z - -2 - and Y -2 - then the value of - z -2-2-2- Y -2- - z -2-2-4-2-8-2- Y -16-2 isA- 100B- 320C- 340D- 400

As we can see, |z|^2+|z 2|^2=4 ⋯ (1) Similarly, |α|^2+|α 4|^2=16 ⋯ (2) |β|^2+|β 8|^2=64 ⋯ (3) |γ|^2+|γ 16|^2=256 ⋯ (4) Adding all the above ...

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Standard XII

Mathematics

Definition of Circle

Let z be an i...

Question

Let $z$ be an imaginary complex number satisfying $| z - 1 | = 1.$ If $α = 2 z,$ $β = 2 α$ and $γ = 2 β,$ then the value of $| z |^{2} + | α |^{2} + | β |^{2} + | γ |^{2} + | z - 2 |^{2} + | α - 4 |^{2} + | β - 8 |^{2} + | γ - 16 |^{2}$ is

100

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320

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340

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400

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Solution

The correct option is C $340$

As we can see,
$| z |^{2} + | z - 2 |^{2} = 4 \dots (1)$
Similarly,
$| α |^{2} + | α - 4 |^{2} = 16 \dots (2)$
$| β |^{2} + | β - 8 |^{2} = 64 \dots (3)$
$| γ |^{2} + | γ - 16 |^{2} = 256 \dots (4)$

Adding all the above equations $(1), (2), (3)$ and $(4)$ ,
$| z |^{2} + | α |^{2} + | β |^{2} + | γ |^{2} + | z - 2 |^{2} + | α - 4 |^{2} + | β - 8 |^{2} + | γ - 16 |^{2} = 340$

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Let z be an imaginary complex number satisfying |z−1|=1. If α=2z, β=2α and γ=2β, then the value of |z|2+|α|2+|β|2+|γ|2+|z−2|2+|α−4|2+|β−8|2+|γ−16|2 is

The correct option is C 340 As we can see, |z|2+|z−2|2=4 ⋯(1) Similarly, |α|2+|α−4|2=16 ⋯(2) |β|2+|β−8|2=64 ⋯(3) |γ|2+|γ−16|2=256 ⋯(4) Adding all the above equations (1),(2),(3) and (4), |z|2+|α|2+|β|2+|γ|2+|z−2|2+|α−4|2+|β−8|2+|γ−16|2=340

Let $z$ be an imaginary complex number satisfying $| z - 1 | = 1.$ If $α = 2 z,$ $β = 2 α$ and $γ = 2 β,$ then the value of $| z |^{2} + | α |^{2} + | β |^{2} + | γ |^{2} + | z - 2 |^{2} + | α - 4 |^{2} + | β - 8 |^{2} + | γ - 16 |^{2}$ is