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Find-the-first-four-terms-in-the-expansion-of-x-3-1-x-2-2-2-x-2-in-ascending-power-of-x-M-m-

Question Number 185449 by Mastermind last updated on 22/Jan/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\frac{\mathrm{x}−\mathrm{3}}{\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} \left(\mathrm{2}+\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{in} \\ $$$$\mathrm{ascending}\:\mathrm{power}\:\mathrm{of}\:\mathrm{x}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$…

Write-down-the-expansion-of-a-cosx-b-1-l-x-and-hence-show-that-cosx-1-x-1-x-x-2-2-x-3-2-13x-4-24-M-m-

Question Number 185450 by Mastermind last updated on 22/Jan/23 $$\mathrm{Write}\:\mathrm{down}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{cosx}\:\left(\mathrm{b}\right)\:\frac{\mathrm{1}}{\mathrm{l}+\mathrm{x}},\:\mathrm{and}\:\mathrm{hence}\:\mathrm{show} \\ $$$$\mathrm{that}\:\frac{\mathrm{cosx}}{\mathrm{1}+\mathrm{x}}\:=\:\mathrm{1}−\mathrm{x}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}+\frac{\mathrm{13x}^{\mathrm{4}} }{\mathrm{24}}+… \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$…

Show-that-1-z-1-z-1-z-1-z-2-1-z-2-1-z-2-Where-z-is-a-complex-number-Help-

Question Number 185401 by Mastermind last updated on 21/Jan/23 $$\mathrm{Show}\:\mathrm{that}\:\frac{\mathrm{1}+\mathrm{z}}{\mathrm{1}−\mathrm{z}}\:+\:\frac{\mathrm{1}+\bar {\mathrm{z}}}{\mathrm{1}−\bar {\mathrm{z}}}\:=\:\frac{\mathrm{2}\left(\mathrm{1}−\mid\mathrm{z}\mid^{\mathrm{2}} \right)}{\mid\mathrm{1}−\mathrm{z}\mid^{\mathrm{2}} } \\ $$$$\mathrm{Where}\:\mathrm{z}\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$ Commented…

i-have-forgotten-my-password-how-may-i-retrieve-it-please-help-me-or-forward-me-to-one-of-the-developers-please-

Question Number 119856 by talminator2856791 last updated on 27/Oct/20 $$\mathrm{i}\:\mathrm{have}\:\mathrm{forgotten}\:\mathrm{my}\:\mathrm{password}. \\ $$$$\mathrm{how}\:\mathrm{may}\:\mathrm{i}\:\mathrm{retrieve}\:\mathrm{it}? \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{or}\:\mathrm{forward}\:\mathrm{me}\:\mathrm{to} \\ $$$$\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{developers}\:\mathrm{please} \\ $$ Commented by mr W last updated on…

lim-z-iz-3-iz-1-2z-3i-z-i-2-M-m-

Question Number 185374 by Mastermind last updated on 20/Jan/23 $$\mathrm{li}\underset{\mathrm{z}\rightarrow\infty} {\mathrm{m}}\frac{\mathrm{iz}^{\mathrm{3}} +\mathrm{iz}−\mathrm{1}}{\left(\mathrm{2z}+\mathrm{3i}\right)\left(\mathrm{z}−\mathrm{i}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$ Answered by MJS_new last…

Question-54226

Question Number 54226 by Meritguide1234 last updated on 31/Jan/19 Commented by Tawa1 last updated on 31/Jan/19 $$\mathrm{Sir},\:\:\mathrm{please}\:\mathrm{send}\:\mathrm{me}\:\mathrm{the}\:\mathrm{question}\:\mathrm{and}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{this}\:\mathrm{question}\:\mathrm{again}. \\ $$$$\:\:\:\:\:\frac{\sqrt{\mathrm{10}\:+\:\sqrt{\mathrm{3}}\:}\:+\:\sqrt{\mathrm{10}\:+\:\sqrt{\mathrm{3}}\:\:}\:+\:..\:\sqrt{\mathrm{10}\:+\:\sqrt{\mathrm{n}}}}{\:\sqrt{\mathrm{10}\:−\:\sqrt{\mathrm{3}}}\:\:+\:\sqrt{\mathrm{10}\:−\:\sqrt{\mathrm{3}}}\:+\:..\:\sqrt{\mathrm{10}\:−\:\sqrt{\mathrm{n}}}} \\ $$$$\mathrm{That}\:\mathrm{is}\:\mathrm{not}\:\mathrm{really}\:\mathrm{the}\:\mathrm{question}\:\mathrm{but}\:\mathrm{something}\:\mathrm{like}\:\mathrm{you}\:\mathrm{posted} \\ $$$$\mathrm{sometimes}\:\mathrm{ago}\:\mathrm{sir}. \\ $$…

Show-that-f-z-z-2-is-harmonic-in-polar-form-

Question Number 185278 by Mastermind last updated on 19/Jan/23 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{z}\right)=\mathrm{z}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{harmonic}\:\mathrm{in} \\ $$$$\mathrm{polar}\:\mathrm{form} \\ $$ Commented by Frix last updated on 19/Jan/23 $$\mathrm{Please}\:\mathrm{tell}\:\mathrm{us}\:\mathrm{the}\:\mathrm{definition}\:\mathrm{of}\:\mathrm{a}\:“\mathrm{harmonic} \\ $$$$\mathrm{function}''\:\mathrm{in}\:\mathrm{complex}\:\mathrm{analysis}.…