complex question

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 ±w.

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

now |z|=|iw|=1

thus |z+iw|≤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.