if |Z| = 1 , then find the value of 1 + z / 1 + z
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Answer:
∣z∣=1
Let z=x+iy
∴
x
2
+y
2
=1
⇒x
2
+y
2
=1
∴
1−z
2
z
=
1−(x
2
−y
2
+2ixy)
x+iy
=
1−x
2
+y
2
−2ixy
x+iy
=
2y
2
−2ixy
x+iy
=
2iy(−iy−x)
x+iy
=
−2iy
1
=
2y
i
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