Maths · Argand diagram
If we plot and on the argand plane, the locus of and are
If we plot \( \left|Z_{1}\right|=2 \) and \( \left|Z_{2}-6-8 i\right|=4 \) on the argand plane, the locus of \( Z_{1} \) and \( Z_{2} \) are
- A. two circle touching each other
- B. two circles neither touching nor intersecting
- C. two circles intersecting
- D. none of these
Step-by-step solution
The locus of |Z1|=2 is a circle centered at the origin with radius 2. The locus of |Z2 - 6 - 8i|=4 is a circle centered at (6,8) with radius 4. The distance between centers is sqrt(6^2+8^2)=10. Since 10 > 2+4=6, the circles are separate and do not intersect or touch.