Answer:
Explanation:
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|z|^2 = |z|*|z| = (|z|)^2
Since the argument of z is pi/4, z can be written as z=r*(cos(pi/4)+i*sin(pi/4)) where r is the magnitude of z.
We also know that |x-w| =sqrt(5).
This means that |z-w| = sqrt(5).
Substituting the expression for z, we get:
|r*(cos(pi/4)+i*sin(pi/4))-w| = sqrt(5)
Simplifying this equation, we get:
|r-2-i| = sqrt(5)
Squaring both sides, we get:
(r-2-i)(r-2+i) = 5
Simplifying, we get:
r^2-4+i(2r-2)=5
Equating the real and the imaginary parts, we get:
r^2-4 = 5
and
2r-2=0
Solving these equations simultaneously, we get:
r = sqrt(9)
Therefore,
|z| = sqrt(9)
Hence,
|z|^2 = (sqrt(9))^2 = 9