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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}.…

Show-that-f-z-z-2-is-uniformly-continous-in-the-region-z-lt-R-where-0-lt-R-lt-Help-

Question Number 185245 by Mastermind last updated on 19/Jan/23 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{z}\right)=\mathrm{z}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{uniformly} \\ $$$$\mathrm{continous}\:\mathrm{in}\:\mathrm{the}\:\mathrm{region}\:\mid\mathrm{z}\mid<\mathrm{R} \\ $$$$\mathrm{where}\:\mathrm{0}<\mathrm{R}<\infty. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$ Commented by…

Using-approach-prove-that-lim-z-i-3z-4-2z-3-8z-2-2z-5-z-i-4-4i-Help-

Question Number 185243 by Mastermind last updated on 19/Jan/23 $$\mathrm{Using}\:\varepsilon−\delta\:\mathrm{approach}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{li}\underset{\mathrm{z}\rightarrow\mathrm{i}} {\mathrm{m}}\frac{\mathrm{3z}^{\mathrm{4}} −\mathrm{2z}^{\mathrm{3}} +\mathrm{8z}^{\mathrm{2}} −\mathrm{2z}+\mathrm{5}}{\mathrm{z}−\mathrm{i}}=\mathrm{4}+\mathrm{4i} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$ Commented by Frix…