Los (pi+i)^100 op

$$( \pi + i ) ^ { 100 }$$

Evalueren

$$\left(\pi +i\right)^{100}\approx 5,34082733 \cdot 10^{51}-3,646173448 \cdot 10^{51}i$$

Uitbreiden

$$-161700\pi ^{97}i-75287520\pi ^{5}i-16007560800\pi ^{93}i-1902231808400\pi ^{9}i-141629804643600\pi ^{89}i-7110542499799200\pi ^{13}i-253338471349988640\pi ^{85}i-6650134872937201800\pi ^{17}i-132341572939212267400\pi ^{81}i-2041841411062132125600\pi ^{21}i-24865270306254660391200\pi ^{77}i-242519269720337121015504\pi ^{25}i-1917353200780443050763600\pi ^{73}i-12410847811948286545336800\pi ^{29}i-66324638306863423796047200\pi ^{69}i-294692427022540894366527900\pi ^{33}i-1095067153187962886461165020\pi ^{65}i-3420029547493938143902737600\pi ^{37}i-9013924030034630492634340800\pi ^{61}i-20116440213369968050635175200\pi ^{41}i-38116532895986727945334202400\pi ^{57}i-61448471214136179596720592960\pi ^{45}i-84413487283064039501507937600\pi ^{53}i-98913082887808032681188722800\pi ^{49}i-100\pi i+3921225\pi ^{4}+3921225\pi ^{96}[phone]\pi ^{8}[phone]\pi ^{92}+1050421051106700\pi ^{12}+1050421051106700\pi ^{88}+1345860629046814650\pi ^{16}+1345860629046814650\pi ^{84}+535983370403809682970\pi ^{20}+535983370403809682970\pi ^{80}+79776075565900368755100\pi ^{24}+79776075565900368755100\pi ^{76}+4998813702034726525205100\pi ^{28}+4998813702034726525205100\pi ^{72}+143012501349174257560226775\pi ^{32}+143012501349174257560226775\pi ^{68}+1977204582144932989443770175\pi ^{36}+1977204582144932989443770175\pi ^{64}+13746234145802811501267369720\pi ^{40}+13746234145802811501267369720\pi ^{60}+49378235797073715747364762200\pi ^{44}+49378235797073715747364762200\pi ^{56}+93206558875049876949581681100\pi ^{48}+93206558875049876949581681100\pi ^{52}+\pi ^{100}-4950\pi ^{2}-4950\pi ^{98}-1192052400\pi ^{6}-1192052400\pi ^{94}-17310309456440\pi ^{10}-17310309456440\pi ^{90}-44186942677323600\pi ^{14}-44186942677323600\pi ^{86}-30664510802988208300\pi ^{18}-30664510802988208300\pi ^{82}-7332066885177656269200\pi ^{22}-7332066885177656269200\pi ^{78}-699574816500972464467800\pi ^{26}-699574816500972464467800\pi ^{74}-29372339821610944823963760\pi ^{30}-29372339821610944823963760\pi ^{70}-580717429720889409486981450\pi ^{34}-580717429720889409486981450\pi ^{66}-5670048986634686922786117600\pi ^{38}-5670048986634686922786117600\pi ^{62}-28258808871162574166368460400\pi ^{42}-28258808871162574166368460400\pi ^{58}-73470998190814997343905056800\pi ^{46}-73470998190814997343905056800\pi ^{54}-100891344545564193334812497256\pi ^{50}+1+100\pi ^{99}i+161700\pi ^{3}i+75287520\pi ^{95}i+16007560800\pi ^{7}i+1902231808400\pi ^{91}i+141629804643600\pi ^{11}i+7110542499799200\pi ^{87}i+253338471349988640\pi ^{15}i+6650134872937201800\pi ^{83}i+132341572939212267400\pi ^{19}i+2041841411062132125600\pi ^{79}i+24865270306254660391200\pi ^{23}i+242519269720337121015504\pi ^{75}i+1917353200780443050763600\pi ^{27}i+12410847811948286545336800\pi ^{71}i+66324638306863423796047200\pi ^{31}i+294692427022540894366527900\pi ^{67}i+1095067153187962886461165020\pi ^{35}i+3420029547493938143902737600\pi ^{63}i+9013924030034630492634340800\pi ^{39}i+20116440213369968050635175200\pi ^{59}i+38116532895986727945334202400\pi ^{43}i+61448471214136179596720592960\pi ^{55}i+84413487283064039501507937600\pi ^{47}i+98913082887808032681188722800\pi ^{51}i$$