1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# For all complex numbers z1,z2 satisfying |z1|=12 and |z2âˆ’3âˆ’4i|=5, then minimum value of |z1âˆ’z2| is

A
0
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
7
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
17
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is B 2Given:-z1 and z2 are the complex number.|z1|=12|z2−3−4i|=5To find minimum value of |z1−z2|Solution:-We know that|z1−z2|≥|z1|−|z2|and|z2−3−4i|≥|z2|−|3+4i||z2−3−4i|≥|z2|−√(3)2+(4)2{|a+bi|}=√a2+b25≥|z2|−5|z2|≥10 for minimum value.z2=10∴minimum value of |z1−z2|≥|z1|−|z2||z1−z2|≥12−10|z1−z2|≥2 Hence the minimum value of |z1|−|z2|=2

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Properties of Modulus
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program