If |z-2-i|=4 then find the minimum value of |3z-6+15i| plz reply fast as possible
Riya , 7 Years ago
Grade 12
Algebra> If |z-2-i|=4 then find the minimum value ...
2 Answerskashish bhatia
Last Activity: 7 Years ago
|z-2-i|=4z-2-i=+4,-4z=6+i,(-2+i)1.z=6+i|3(6+i)-6+15i|=|12+18i|2.z= -2+I|3(-2+i)-6+15i|=|12-18i|=MINIMUM
Samyak Jain
Last Activity: 7 Years ago
|z – 2 – i| = 4 or |z – (2 + i)| = 4
Above equation represents a circle centred at (2,1) with radius 4 units.
Minimum value of |3z-6+15i| means minimum value of
3|z – (2 – 5i)|.
First we’ll find the minimum value of |z – (2 – 5i)| & multiply it by 3.
It denotes least distance from a point on the circle & point (2, – 5).
(2, – 5) lies below the circle in coordinate axes system.
Line through center (2,1) & (2, – 5) is parallel to y-axis &
its eqn is x = 2 …................(2)
points of intersection of (1) & (2) are (2,5) & (2, – 3).
By geometry, (2, –3) is nearest to (2, –5) of all points on the circle.
minimum value of |z – (2 – 5i)| is 2 and hence
the minimum value of |3z-6+15i| = 3|z – (2 – 5i)| = 3*2
= 6
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