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The complex number z having least positi...

The complex number z having least positive argument which satisfy the condition `|z - 25i| <= 15` is

Text Solution

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With the given condition `|z-25i| le 15`, we can draw a circle with center `(0,25)` and radius `15`.
Please refer to video for the figure.
From the figure, we can see that,
`P` point will have least positive argument.
Here, `CP = 15, OC = 25 and /_CPO = 90^@`
Then, `OP^2 =OC^2- CP^2 = 25^2-15^2 = 400`
`=>OP = 20`
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