questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Complex Numbers
Question 349
Question 349 of 455
Medium
MCQ
If
z
−
4
z
=
2
z-\dfrac4z=2
z
−
z
4
=
2
, then the maximum value of
∣
z
∣
|z|
∣
z
∣
is equal to:
A
5
+
1
\sqrt{5}+1
5
+
1
B
2
C
2
+
2
2+\sqrt{2}
2
+
2
D
3
+
1
\sqrt{3}+1
3
+
1
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
∣
z
∣
≤
∣
z
−
4
z
∣
+
4
∣
z
∣
=
2
+
4
∣
z
∣
⟹
∣
z
∣
2
−
2
∣
z
∣
−
4
≤
0
⟹
∣
z
∣
≤
1
+
5
.
|z|\le\left|z-\dfrac4z\right|+\dfrac4{|z|}=2+\dfrac4{|z|} \implies |z|^2-2|z|-4\le0 \implies |z|\le1+\sqrt{5}.
∣
z
∣
≤
z
−
z
4
+
∣
z
∣
4
=
2
+
∣
z
∣
4
⟹
∣
z
∣
2
−
2∣
z
∣
−
4
≤
0
⟹
∣
z
∣
≤
1
+
5
.
Maximum value:
5
+
1.
\sqrt{5}+1.
5
+
1.
Answer the question to unlock
Previous
Next