Geometrical Representation of Algebra of Complex Numbers
lf the real p...
Question
lf the real part of z−4z−2i(z≠2i) is zero then the locus of z is?
A
(x−2)2+(y−1)2=25
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(x+2)2+(y−1)2=5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(x−2)2+(y+1)2=5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(x−2)2+(y−1)2=5 excluding the point (0,2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is D(x−2)2+(y−1)2=5 excluding the point (0,2) Re(z−4z−2i)=0 z−4z−2i+¯¯¯z−4¯¯¯z+2i=0 [∵z+¯¯¯z=Re(z)=0] z¯¯¯z+2iz−4¯¯¯z−8i+z¯¯¯z−4z−2i¯¯¯z−8i=0 |z|2+2i(z−¯¯¯z)−4(z+¯¯¯z)=0 Letz=x+iy ⇒2(x2+y2)+2i(2iy)−2(2x)=0 ⇒(x−2)2+(y−1)2=22+12 =5