1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Conjugate of a Complex Number
If z = a+ib s...
Question
If
z
=
a
+
i
b
satisfy
(
4
+
2
i
)
z
+
(
8
−
2
i
)
z
′
=
−
2
+
10
i
,
where
z
′
is the complex conjugate of
z
, then the value of
|
a
+
2
b
|
is
Open in App
Solution
Given :
(
4
+
2
i
)
z
+
(
8
−
2
i
)
z
′
=
−
2
+
10
i
z
=
a
+
i
b
,
z
′
=
a
−
i
b
Now,
(
4
+
2
i
)
z
+
(
8
−
2
i
)
z
′
=
−
2
+
10
i
⇒
4
(
z
+
2
z
′
)
+
2
i
(
z
−
z
′
)
=
−
2
+
10
i
⇒
4
(
3
a
−
i
b
)
−
4
b
=
−
2
+
10
i
⇒
(
12
a
−
4
b
)
−
i
(
4
b
)
=
−
2
+
10
i
⇒
12
a
−
4
b
=
−
2
,
−
4
b
=
10
⇒
b
=
−
5
2
,
a
=
−
1
∴
|
a
+
2
b
|
=
6
Suggest Corrections
0
Similar questions
Q.
If
z
=
a
+
i
b
satisfy
(
4
+
2
i
)
z
+
(
8
−
2
i
)
z
′
=
−
2
+
10
i
,
where
z
′
is the complex conjugate of
z
, then the value of
|
a
+
2
b
|
is
Q.
If complex number
z
satisfies
|
z
|
+
z
=
2
+
i
, then
z
is
Q.
If the complex number
z
satisfies
z
+
√
2
|
z
+
1
|
+
i
=
0
, then
z
is :
Q.
The complex number Z satisfies the equation Z +
|
Z
|
= 2+8i, then the value of
|
Z
|
- 8 is
___
Q.
Let
z
is a complex number and
¯
¯
¯
z
is conjugate of
z
. If
(
1
+
i
)
z
=
(
1
−
i
)
¯
¯
¯
z
,
then the value of
z
+
i
¯
¯
¯
z
is
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Conjugate of a Complex Number
MATHEMATICS
Watch in App
Explore more
Conjugate of a Complex Number
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app