Question Number 190199 by 073 last updated on 29/Mar/23
Answered by mr W last updated on 29/Mar/23
$${min}=\mathrm{0}\:{when}\:{z}=\mathrm{4}−\mathrm{3}{i} \\ $$
Commented by 073 last updated on 29/Mar/23
$$\mathrm{but}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{7} \\ $$$$?? \\ $$
Commented by mehdee42 last updated on 29/Mar/23
$${if}\:\:\mid{z}\mid=\mathrm{12}\:\:{then}\:\:{min}\left(\mid{z}−\mathrm{4}+\mathrm{3}{i}\mid\right)=\mathrm{7} \\ $$$${but}\:{if}\:\mid{z}\mid\leqslant\mathrm{12}\:\:{then}\:\:{min}\left(\mid{z}−\mathrm{4}+\mathrm{3}{i}\mid\right)=\mathrm{0} \\ $$$${because}\:\mid{z}\mid\leqslant\mathrm{12}\:{the}\:{set}\:{of}\:{points}\:{inside}\:{and}\:{on}\:{the}\:{circle}\:{has}\:{a}\:{radius}\:{of}\:\mathrm{12} \\ $$$${and}\:{point}\:{z}_{\mathrm{0}} =−\mathrm{4}+\mathrm{3}{i}\:{is}\:{inside}\:{this}\: \\ $$$${circle}. \\ $$
Commented by mehdee42 last updated on 29/Mar/23
$${certainly}\:,\:\mathrm{0} \\ $$