Question

l'
11. Find the locus of complex number z=x+iy, If
| z-(3-4i) | =7
​

Answer 1

Answer:

Let z=x+iy

then  

∣

∣

∣

∣

∣

∣

​  

 

z+3i

z−3i

​  

 

∣

∣

∣

∣

∣

∣

​  

≤  

2

​  

 

∣

∣

∣

∣

∣

∣

​  

 

x+iy+3i

x+iy−3i

​  

 

∣

∣

∣

∣

∣

∣

​  

≤  

2

​  

 

∣

∣

∣

∣

∣

∣

​  

 

x+i(y+3)

x+i(y−3)

​  

 

∣

∣

∣

∣

∣

∣

​  

≤  

2

​  

 

x  

2

+(y−3)  

2

 

​  

≤  

2

​  

 

x  

2

+(y+3)  

2

 

​  

 

On squaring on both sides, we get

x  

2

+(y−3)  

2

≤2(x  

2

+(y+3)  

2

)

x  

2

+y  

2

+9−6y≤2x  

2

+2y  

2

+18+12y

x  

2

+y  

2

+18y+9≥0

A circle with centre (0,−9) and radius 6  

2

​  

units.

Step-by-step explanation: