plot for mod z-i = 2
Answers
To say
|
z
−
i
|
=
2
is to say that the (Euclidean) distance between
z
and
i
is
2
.
graph{(x^2+(y-1)^2-4)(x^2+(y-1)^2-0.011) = 0 [-5.457, 5.643, -1.84, 3.71]}
Alternatively, use the definition:
|
z
|
=
√
z
¯
z
Consider
z
=
x
+
y
i
where
x
and
y
are Real.
Then
2
=
|
z
−
i
|
=
|
x
+
y
i
−
i
|
=
|
x
+
(
y
−
1
)
i
|
=
√
(
x
+
(
y
−
1
)
i
)
(
x
−
(
y
−
1
)
i
)
=
√
x
2
+
(
y
−
1
)
2
Square both ends and transpose to get:
x
2
+
(
y
−
1
)
2
=
2
2
which is the equation of a circle radius
2
with centre
(
0
,
1
)
, i.e.
i
.
Hope it helps
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Answer:
This is a circle with radius 2 and centre i
Step-by-step explanation:
To say |z−i|=2 is to say that the (Euclidean) distance between z and i is 2.
graph{(x^2+(y-1)^2-4)(x^2+(y-1)^2-0.011) = 0 [-5.457, 5.643, -1.84, 3.71]}
Alternatively, use the definition:
|z|=√z¯z
Consider z=x+yi where x and y are Real.
Then
2=|z−i|=|x+yi−i|=|x+(y−1)i|
=√(x+(y−1)i)(x−(y−1)i)=√x2+(y−1)2
Square both ends and transpose to get:
x2+(y−1)2=22
which is the equation of a circle radius 2 with centre (0,1), i.e. i.