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Grade: 12th pass
        
Hi please solve above 2 problems kindly .i hope you can understand thankyou
2 months ago

Answers : (1)

Aditya Gupta
823 Points
							
note that |z1|^2=4 |z2|^2=9 and |z3|^2=16
also |z|^2= z*zbar
simply write |4z2z3+9z1z3+16z1z2|=|z1*z1barz2z3+z2*z2barz1z3+z3*z3barz1z2|
=|z1||z2||z3||z1bar+z2bar+z3bar|
=2*3*4*|(z1+z2+z3)whole bar|
=24*|(z1+z2+z3)|
=24*5
=120
in second question simply apply geometry and draw a circle with centre i and radius 5 in the argand plane. then write |iz+z1| as |z – iz1| which represents the distance between z and iz1. you will find that iz1 lies on the circumference of the circle described above. so obviously the minimum and max distances between z and iz1 can be 0 and 2*r=2*5= 10 respectively
2 months ago
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