The complex number z having least positive argument which satisfy the – InterviewSolution

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1.	The complex number z having least positive argument which satisfy the condition `\|z - 25i\|
Answer» 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` Let `/_POC = theta` Then, `sintheta = 15/25 = 3/5, cos theta = 20/25 = 4/5` So, coordinates of point `P` will be `(OP sintheta,OPcostheta)`. Coordinates of `P` are `(20(3/5),20(4/5))` that is `(12,16)`. If we convert it into a complex number, then it will be `12+16i`, which is the required number.

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