Question Number 69020 by mhmd last updated on 17/Sep/19
$${if}\:{z}=\left(\mathrm{2}+\mathrm{3}{i}/\mathrm{3}−\sqrt{−\mathrm{4}}\right)^{\mathrm{17}} \:{by}\:{using}\:{demover}\:{find}\:\left({z}−\mathrm{1}\right)^{−\mathrm{5}} \: \\ $$$${pleas}\:{sir}\:{help}\:{me}\:? \\ $$
Commented by MJS last updated on 17/Sep/19
$$\mathrm{please}\:\mathrm{set}\:\left(\right)\:\mathrm{correctly} \\ $$$$\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:{z}=\left(\frac{\mathrm{2}+\mathrm{3}{i}}{\mathrm{3}−\sqrt{−\mathrm{4}}}\right)^{\mathrm{17}} ? \\ $$$$\frac{\mathrm{2}+\mathrm{3}{i}}{\mathrm{3}−\mathrm{2}{i}}={i} \\ $$$${i}^{\mathrm{17}} ={i} \\ $$$$\left(−\mathrm{1}+{i}\right)^{−\mathrm{5}} =\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{8}}{i} \\ $$