complex question

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Let z and w be two complex numbers such that |z|=|w|=1
and |z+iw|=|z-iw|=2. then z=

#Mathematics #Algebra

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3 Answers

36

rahul ·2012-04-04 22:10:09

is it something like ....
âˆš4 - w²

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21

Swaraj Dalmia ·2012-04-04 23:43:52

I think that the soln. does not exist.
|z|=|w|=|iw|=1
Now to get mod value as 2 the argument of z,iw & that of z,(-iw) should be same.However this means that arg(wi)=arg(-wi) which is impossible.
Hence no soln.

Here the sum and diff. of 2 unit vectors have same mod value hence they must be inclined at 90.The mod value at this pos. will be √2(and not 2 for soln. to exist).The value of z then will be Â±w.

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262

Aditya Bhutra ·2012-04-05 00:07:36

|z+iw| â‰¤|z| +|iw| (equality occurs when both are parallel ie. have same argument)

now |z|=|iw|=1

thus |z+iw|â‰¤2 but |z+iw|=2

hence z = iw

but |z-iw|=2 which is not possible from the above relation ,

hence no such z exists.

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