11:[["$","meta","0",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","meta","1",{"charSet":"utf-8"}],["$","title","2",{"children":"If z = (\\frac{\\sqrt{3} + i}{2}), then (z101 + i103)105 is eq... | MATH - INTEGRAL POWER OF IOTA, ALGEBRAIC OPERATIONS AND EQUALITY OF COMPLEX NUMBERS | SolveeIt | Solveeit"}],["$","meta","3",{"name":"description","content":"If z = (\\frac{\\sqrt{3} + i}{2}), then (z101 + i103)105 is equal to\n Options: z, z², z³, None of these, Need help? Chat with our AI do..."}],["$","meta","4",{"name":"application-name","content":"Solveeit"}],["$","meta","5",{"name":"author","content":"SolveeIt Team"}],["$","link","6",{"rel":"manifest","href":"/manifest.json","crossOrigin":"use-credentials"}],["$","meta","7",{"name":"keywords","content":"AI doubt solver,JEE NEET AI tutor,accurate exam solutions,verified answer platform,doubt solver,AI tutor,IIT JEE preparation online,NEET UG exam help,engineering entrance solutions,medical entrance doubts,JEE preparation,NEET preparation,exam preparation,entrance exam,engineering entrance,medical entrance,best AI for JEE questions,NEET physics chemistry biology doubts,24/7 doubt solving for exams,step-by-step problem solutions,JEE questions,NEET questions,better than doubtnut,alternative to byjus,chegg replacement for JEE,JEE preparation India,NEET coaching online India,AI tutor for Indian students,JEE main advanced mathematics,NEET UG biology questions,physics numerical solver,chemistry organic reactions helper,MH CET preparation,BITSAT preparation,CET exam,IIT Bombay,BITS Pilani,IIT JEE,AIIMS preparation,top college preparation,error-free solutions,IIT alumni verified answers,real-time doubt clearing,exam pattern specific practice"}],["$","meta","8",{"name":"creator","content":"SolveeIt"}],["$","meta","9",{"name":"publisher","content":"SolveeIt"}],["$","meta","10",{"name":"robots","content":"index, follow"}],["$","meta","11",{"name":"googlebot","content":"index, follow, max-video-preview:-1, max-image-preview:large, max-snippet:-1"}],["$","link","12",{"rel":"canonical","href":"https://solveeit.ai/question/if-z-fracsqrt3-i2-then-zsup101sup-isup103supsup105"}],["$","meta","13",{"name":"format-detection","content":"telephone=no, date=no, address=no, email=no, url=no"}],["$","meta","14",{"name":"apple-mobile-web-app-capable","content":"yes"}],["$","meta","15",{"name":"apple-mobile-web-app-title","content":"Solveeit - AI Doubt Solver"}],["$","meta","16",{"name":"apple-mobile-web-app-status-bar-style","content":"black-translucent"}],["$","meta","17",{"property":"og:title","content":"If z = (\\frac{\\sqrt{3} + i}{2}), then (z101 + i103)105 is eq... | MATH - INTEGRAL POWER OF IOTA, ALGEBRAIC OPERATIONS AND EQUALITY OF COMPLEX NUMBERS | SolveeIt"}],["$","meta","18",{"property":"og:description","content":"If z = (\\frac{\\sqrt{3} + i}{2}), then (z101 + i103)105 is equal to\n Options: z, z², z³, None of these, Need help? Chat with our AI do..."}],["$","meta","19",{"property":"og:url","content":"https://solveeit.ai/question/if-z-fracsqrt3-i2-then-zsup101sup-isup103supsup105"}],["$","meta","20",{"property":"og:image","content":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2116.png?top_left_x=1064&top_left_y=1712&width=532&height=283&app=solveeit"}],["$","meta","21",{"property":"og:image:width","content":"1200"}],["$","meta","22",{"property":"og:image:height","content":"630"}],["$","meta","23",{"property":"og:image:alt","content":"If z = (\\frac{\\sqrt{3} + i}{2}), then (z101 + i103)105 is eq... | MATH - INTEGRAL POWER OF IOTA, ALGEBRAIC OPERATIONS AND EQUALITY OF COMPLEX NUMBERS | SolveeIt"}],["$","meta","24",{"property":"og:type","content":"article"}],["$","meta","25",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","26",{"name":"twitter:title","content":"If z = (\\frac{\\sqrt{3} + i}{2}), then (z101 + i103)105 is eq... | MATH - INTEGRAL POWER OF IOTA, ALGEBRAIC OPERATIONS AND EQUALITY OF COMPLEX NUMBERS | SolveeIt"}],["$","meta","27",{"name":"twitter:description","content":"If z = (\\frac{\\sqrt{3} + i}{2}), then (z101 + i103)105 is equal to\n Options: z, z², z³, None of these, Need help? Chat with our AI do..."}],["$","meta","28",{"name":"twitter:image","content":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2116.png?top_left_x=1064&top_left_y=1712&width=532&height=283&app=solveeit"}],["$","link","29",{"rel":"icon","href":"/favicon.ico","type":"image/x-icon","sizes":"16x16"}],["$","meta","30",{"name":"next-size-adjust"}]]

Question: If z = \(\frac{\sqrt{3} + i}{2}\), then (z<sup>101</sup> + i<sup>103</sup>)<sup>105</sup> is equal t...

Solution