First slide

Geometry of complex numbers

Question

If |z₁| = 15 and |z₂ - 3 - 4i| = 5, then

Moderate

A

${|z_{1} - z_{2}|}_{min} = 5$
B

${|z_{1} - z_{2}|}_{min} = 10$
C

${|z_{1} - z_{2}|}_{max} = 20$
D

${|z_{1} - z_{2}|}_{max} = 25$

Solution

We have, $|z_{1}| = 15, |z_{2} - 3 - 4 i| = 5$
Minimum value of |z₁ - z₂| is AB = OB - OA = 15 - 10 = 5.
Maximum value of |z₁ - z₂| is CA = OA + OC = 10 + 15 = 25.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App