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Byju's Answer
Standard XII
Mathematics
Higher Order Derivatives
if z+√(2)|z+1...
Question
if z+\sqrt2\vert z+1\vert+i=o, where i=\sqrt{-1}, then \vert Re(z)+Im(z)\vert is
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Q.
Assertion :If
z
=
√
3
+
4
i
+
√
−
3
+
4
i
, then principal arg of z i.e. arg (z) are
±
π
4
,
±
3
π
4
where
√
−
1
=
i
. Reason: If z = A + iB, then
√
z
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
√
|
z
|
+
R
e
(
z
)
2
+
i
√
|
z
|
−
R
e
(
z
)
2
,
if
B
>
0
⎷
|
z
|
+
R
e
(
z
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2
−
i
√
|
z
|
−
R
e
(
z
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2
,
if
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<
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Q.
If
sin
θ
=
(
z
−
1
i
)
,
where
z
is non real,
θ
represents angle of a triangle, then
Q.
If
|
z
|
=
1
and
z
1
−
z
3
z
2
−
z
3
=
z
−
i
z
+
i
then
z
1
,
z
2
,
z
3
will be vertices of a
Q.
If
z
=
(
i
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i
, where
i
=
√
−
1
, then Re(z) is:
