Friday, November 15, 2013
|z−3|=1
What does |z−3|=1 look like ? A circle of radius 1, centered at 3.
What does |1z−3|=1 look like ?
|1z−3|=1|1−3zz|2=1|1−3z|2=|z|2(1−3z)¯(1−3z)=z¯z(1−3z)(1−3¯z)=z¯z1−3z−3¯z+9z¯z=z¯z8z¯z−3z−3¯z+1=0z¯z−38z−38¯z+18=0(z−38)(¯z−38)−3282+18=0|z−38|2=164|z−38|=18 |
More at Analysis of a Complex Kind.