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If|z| = 2 and the locus of 5z-1 is the ...

If`|z|` = 2 and the locus of 5z-1 is the circle having radius 'a' and `z_1^2 + z_2^2 - 2 z_1 z_2 cos theta = 0` then `|z_1| : |z_2|` =

Text Solution

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We are given, `|z| = 2`
Let `z_2 = 5z-1`
`=>z_2 +1 = 5z`
`=>|z_2+1| = |5z| = 5|z|`
`=>|z_2-(-1)| = 10`
So, `z_2` is a circle with with `C(-1,0)` and radius `10`.
Now, we are also given,
`z_1^2+z_2^2-2z_1z_2cos theta = 0`
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