Find the square
Toot of complex
Number z=2i
Answers
Answered by
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√
2
i
=
{
1
+
i
,
−
1
−
i
}
Let us look at some details.
Let
z
=
√
2
i
.
(Note that
z
are complex numbers.)
by squaring,
⇒
z
2
=
2
i
by using the exponential form
z
=
r
e
i
θ
,
⇒
r
2
e
i
(
2
θ
)
=
2
i
=
2
e
i
(
π
2
+
2
n
π
)
⇒
{
r
2
=
2
⇒
r
=
√
2
2
θ
=
π
2
+
2
n
π
⇒
θ
=
π
4
+
n
π
So,
z
=
√
2
e
i
(
π
4
+
n
π
)
by Eular's Formula:
e
i
θ
=
cos
θ
+
i
sin
θ
⇒
z
=
√
2
[
cos
(
π
4
+
n
π
)
+
i
sin
(
π
4
+
n
π
)
]
=
√
2
(
±
1
√
2
±
1
√
2
i
)
=
±
1
±
i
I kept the following original post just in case someone needs it.
(
2
i
)
1
2
=
(
2
)
1
2
(
i
)
1
2
,
(
i
)
1
2
= -1
(
2
i
)
1
2
=
(
2
)
1
2
x -1
(
2
)
1
2
= 1.41
(
2
i
)
1
2
= 1.41 x -1 = -1.41
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