If -z-1 and -1-1 where z- then the largest set of values of -2z-1-2-2-1-2 equals

Least distance and greatest distance of any z and ω from the point (12,0) are 12 and 32 respectively. ∴(12)^2+(12)^2≤|z 12|^2+|ω 12|^2≤(32)^2+(32)^2 Hence, 2≤ ...

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Byju's Answer

Standard XIII

Mathematics

Equation of Circle in Complex Form

If |z|=1 and ...

Question

If $| z | = 1$ and $| ω - 1 | = 1$ where $z, ω \in C,$ then the largest set of values of $| 2 z - 1 |^{2} + | 2 ω - 1 |^{2}$ equals

[1, 9]

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[2, 6]

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[2, 12]

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[2, 18]

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Solution

The correct option is D $[2, 18]$
Least distance and greatest distance of any $z$ and $ω$ from the point $(\frac{1}{2}, 0)$ are $\frac{1}{2}$ and $\frac{3}{2}$ respectively.

$∴ {(\frac{1}{2})}^{2} + {(\frac{1}{2})}^{2} \leq {∣ ∣ ∣ z - \frac{1}{2} ∣ ∣ ∣}^{2} + {∣ ∣ ∣ ω - \frac{1}{2} ∣ ∣ ∣}^{2} \leq {(\frac{3}{2})}^{2} + {(\frac{3}{2})}^{2}$
Hence, $2 \leq | 2 z - 1 |^{2} + | 2 ω - 1 |^{2} \leq 18$

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If |z|=1 and |ω−1|=1 where z,ω∈C, then the largest set of values of |2z−1|2+|2ω−1|2 equals

The correct option is D [2,18]Least distance and greatest distance of any z and ω from the point (12,0) are 12 and 32 respectively. ∴(12)2+(12)2≤∣∣∣z−12∣∣∣2+∣∣∣ω−12∣∣∣2≤(32)2+(32)2 Hence, 2≤|2z−1|2+|2ω−1|2≤18

If $| z | = 1$ and $| ω - 1 | = 1$ where $z, ω \in C,$ then the largest set of values of $| 2 z - 1 |^{2} + | 2 ω - 1 |^{2}$ equals