Question Number 32049 by rahul 19 last updated on 18/Mar/18
$$\boldsymbol{{I}}{f}\:\mid\boldsymbol{{z}}−\mathrm{6}−\mathrm{8}\boldsymbol{{i}}\mid\leqslant\mathrm{4}\:{then}\:\boldsymbol{{M}}{inimum}\:{value} \\ $$$${of}\:\mid\boldsymbol{{z}}\mid\:{is}\: \\ $$$$\left.{A}\right)\:\mathrm{4}\: \\ $$$$\left.{B}\right)\:\mathrm{5} \\ $$$$\left.{C}\right)\:\mathrm{6} \\ $$$$\left.{D}\right)\:\mathrm{8}. \\ $$
Answered by mrW2 last updated on 18/Mar/18
$$\sqrt{\mathrm{6}^{\mathrm{2}} +\mathrm{8}^{\mathrm{2}} }−\mathrm{4}=\mathrm{6} \\ $$$$\left.\Rightarrow{answer}\:{C}\right) \\ $$
Commented by rahul 19 last updated on 18/Mar/18
$${thank}\:{u}\:{sir}! \\ $$
Answered by Tinkutara last updated on 18/Mar/18
Commented by Tinkutara last updated on 18/Mar/18
$${In}\:{question}\:\mid{z}−\mathrm{6}−\mathrm{8}{i}\mid\leqslant\mathrm{4} \\ $$$${you}\:{wrote}\:\mid{z}−\mathrm{6}−\mathrm{8}{i}\mid\leqslant\mid{z}\mid+\mid−\mathrm{6}−\mathrm{8}{i}\mid \\ $$$${In}\:{general}\:{a}\leqslant{b}\:{and}\:{a}\leqslant{c}\nRightarrow{b}={c} \\ $$$${e}.{g}.\:\mathrm{5}\leqslant\mathrm{10}\:{and}\:\mathrm{5}\leqslant\mathrm{20}\:{but}\:\mathrm{10}\neq\mathrm{20} \\ $$$${We}\:{cannot}\:{compare}\:{b}\:{and}\:{c}. \\ $$
Commented by rahul 19 last updated on 18/Mar/18
$${check}\:{my}\:{method}\:,\:{where}\:{am}\:{i}\:{wrong}? \\ $$
Commented by rahul 19 last updated on 18/Mar/18
$${ok},{thanks}! \\ $$
Commented by Tinkutara last updated on 18/Mar/18
Locus of z is a circle and its inside. Hence calculating the minimum distance from origin.