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Question Number 69020 by mhmd last updated on 17/Sep/19

if z=(2+3i/3−(√(−4)))^(17)  by using demover find (z−1)^(−5)    pleas sir help me ?

$${if}\:{z}=\left(\mathrm{2}+\mathrm{3}{i}/\mathrm{3}−\sqrt{−\mathrm{4}}\right)^{\mathrm{17}} \:{by}\:{using}\:{demover}\:{find}\:\left({z}−\mathrm{1}\right)^{−\mathrm{5}} \: \\ $$$${pleas}\:{sir}\:{help}\:{me}\:? \\ $$

Commented by MJS last updated on 17/Sep/19

please set () correctly  do you mean z=(((2+3i)/(3−(√(−4)))))^(17) ?  ((2+3i)/(3−2i))=i  i^(17) =i  (−1+i)^(−5) =(1/8)+(1/8)i

$$\mathrm{please}\:\mathrm{set}\:\left(\right)\:\mathrm{correctly} \\ $$$$\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:{z}=\left(\frac{\mathrm{2}+\mathrm{3}{i}}{\mathrm{3}−\sqrt{−\mathrm{4}}}\right)^{\mathrm{17}} ? \\ $$$$\frac{\mathrm{2}+\mathrm{3}{i}}{\mathrm{3}−\mathrm{2}{i}}={i} \\ $$$${i}^{\mathrm{17}} ={i} \\ $$$$\left(−\mathrm{1}+{i}\right)^{−\mathrm{5}} =\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{8}}{i} \\ $$

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