16:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 17:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 15:T4fe,{"@context":"https://schema.org","@type":"Quiz","name":"Jee Main 2021 Complex Numbers PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/jee-main/questions/2021/mathematics/complex-numbers/1kru4nljk","educationalLevel":"Entrance exam preparation","about":"Jee Main / Mathematics / Complex Numbers","hasPart":{"@type":"Question","name":"Jee Main 2021 Complex Numbers PYQ with Solution","text":"Let n denote the number of solutions of the equation z 2 + 3\\overline z = 0, where z is a complex number. Then the value of \\sum\\limits_{k = 0}^\\infty {{1 \\over {{n^k}}}} is equal to :","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"B"},"comment":{"@type":"Comment","text":"z 2 + 3\\overline z = 0 Put z = x + iy \\Rightarrow x 2 - y 2 + 2ixy + 3(x - iy) = 0 \\Rightarrow (x 2 - y 2 + 3x) + i(2xy - 3y) = 0 + i0 \\therefore x 2 - y 2 + 3x = 0 ..... (1) 2xy - 3y = 0 ..... (2) x = {3 \\over 2}, y = 0 Put x = {3 \\over 2} in equation (1) {9 \\over 4} - {y^2} + {9 \\over 2} = 0 {y^2} = {{27} \\over 4} \\Rightarrow y = \\pm {{3\\sqrt 3 } \\over 2} \\therefore (x,y) = \\left( {{3 \\over 2},{{3\\sqrt 3 } \\over 2}} \\right),\\left( {{3 \\over 2},{{ - 3\\sqrt 3 } \\over 2}} \\right) Put y = 0 \\Righ..."}}}18:T484,z² + 3$$\overline z $$ = 0

Put z = x + iy

$$\Rightarrow$$ x² $$-$$ y² + 2ixy + 3(x $$-$$ iy) = 0

$$\Rightarrow$$ (x² $$-$$ y² + 3x) + i(2xy $$-$$ 3y) = 0 + i0

$$\therefore$$ x

Complex Numbers

Continue this paper

Similar Complex Numbers PYQs

More practice from this question