Question Number 6932 by FilupSmith last updated on 03/Aug/16 $$\mathrm{If}\:\mathrm{a}\:\mathrm{vector}\:\boldsymbol{{v}}\:\mathrm{exists}\:\mathrm{in}\:{n}\:\mathrm{dimensions}: \\ $$$$\boldsymbol{{v}}\in\mathbb{R}^{{n}} \\ $$$$\mathrm{Can}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{dimension}\left(\mathrm{s}\right)? \\ $$ Commented by nburiburu last updated on 04/Aug/16 $${you}\:{mean}\:{if}\:{v}\in\mathbb{R}^{{n}} \:\Rightarrow{v}\in\mathbb{C}^{{n}}…
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Question Number 6737 by FilupSmith last updated on 19/Jul/16 $$\mathrm{If}\:{z}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{function}, \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{following}\:\mathrm{true}: \\ $$$$\int{zdx}=\int\Re\left({z}\right){dx}+{i}\int\Im\left({z}\right){dx} \\ $$ Commented by prakash jain last updated on 19/Jul/16 $$\mathrm{Yes}.\:\mathrm{Since}\:{i}\:\mathrm{is}\:\mathrm{simply}\:\mathrm{a}\:\mathrm{constant}.…
Question Number 6512 by Rasheed Soomro last updated on 30/Jun/16 $${Find}\:{complex}\:{number}\:{whose}\:{additive}\: \\ $$$${inverse}\:{is}\:{equal}\:{to}\:{its}\:{multiplicative} \\ $$$${inverse}. \\ $$ Commented by Temp last updated on 30/Jun/16 $$\mathrm{What}\:\mathrm{is}\:\mathrm{additive}\:\mathrm{and}\:\mathrm{multiplicitive}…
Question Number 137275 by mnjuly1970 last updated on 31/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:……{complex}\:\:{analysis}….. \\ $$$$\:\:\:\:{if}\:,\:\:{f}\left(\alpha,{n},{x}\right)=\frac{{d}^{\:{n}} }{{dx}^{{n}} }\left(\alpha^{{x}} \right)\:\:,\:{x}\in\mathbb{C} \\ $$$$\:\:\:\:\:\alpha\in\mathbb{C}−\left\{\mathrm{0}\right\}\:,\:{n}\in\mathbb{C}−\mathbb{Z}^{−} \cup\left\{\mathrm{0}\right\} \\ $$$$\:\:\:\:\:{and}\:\:{g}\left({n},{x}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}} {f}\left(\alpha,{n},{x}\right){d}\alpha \\ $$$$\:\:\:\:\:{then}\:\:{find}\:\:{the}\:{value}\:{of}\:… \\…
Question Number 6044 by sanusihammed last updated on 10/Jun/16 $${Find}\:{the}\:{locus}\:{in}\:{the}\:{complex}\:{plain}\:{such}\:{that}\: \\ $$$${arg}\:\left(\frac{{z}}{{z}\:+\:\mathrm{2}}\right)\:=\:\frac{\Pi}{\mathrm{2}} \\ $$$$ \\ $$$${please}\:{help}. \\ $$ Commented by Yozzii last updated on 10/Jun/16…
Question Number 136167 by ZiYangLee last updated on 19/Mar/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{value}\:\mathrm{for}\:\mathrm{the}\:\mathrm{5}^{\mathrm{th}} \\ $$$$\mathrm{root}\:\mathrm{of}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{is}\:−\mathrm{1}+{i}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{another}\:\mathrm{four}\:\mathrm{values}. \\ $$ Answered by mr W last updated on 19/Mar/21 $${one}\:\mathrm{5}^{{th}}…
Question Number 136023 by mathmax by abdo last updated on 18/Mar/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{z}^{\mathrm{2}} } \mathrm{dz}\:\:\mathrm{with}\:\mathrm{z}\:\mathrm{complex} \\ $$ Commented by yutytfjh67ihd last updated on 25/Mar/21…
Question Number 70361 by mind is power last updated on 03/Oct/19 $${Hello}\: \\ $$$${si}\left({x}\right)=−\int_{{x}} ^{\infty} \frac{{sin}\left({x}\right)}{{x}}{dx} \\ $$$${show}\:\int_{\mathrm{0}} ^{+\infty} {x}^{{a}−\mathrm{1}} {si}\left({x}\right){dx}=−\frac{\Gamma\left({a}\right){sin}\left(\frac{\pi{a}}{\mathrm{2}}\right)}{{a}} \\ $$$${hint}\:{ipp}\:+{complex}\:{Analysis} \\ $$…
Question Number 134461 by pticantor last updated on 04/Mar/21 $${soit}\:\left(\boldsymbol{{E}}\right)\:{l}'{equation}\:{complex}: \\ $$$$\boldsymbol{{z}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{pz}}−\boldsymbol{{q}}=\mathrm{0} \\ $$$$\boldsymbol{{p}},\boldsymbol{{q}}\in\mathbb{C} \\ $$$$\boldsymbol{{let}}\:\boldsymbol{{u}}\in\mathbb{C}\backslash\:\boldsymbol{{u}}^{\mathrm{2}} =\boldsymbol{{q}} \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{if}}\:\boldsymbol{{z}}_{\mathrm{1}} ,\boldsymbol{{z}}_{\mathrm{2}} \boldsymbol{{are}}\:\boldsymbol{{solutions}}\:\boldsymbol{{of}}\:\left(\boldsymbol{{E}}\right), \\ $$$$\mid\boldsymbol{{z}}_{\mathrm{1}} \mid+\mid\boldsymbol{{z}}_{\mathrm{2}}…
Question Number 134419 by mohammad17 last updated on 03/Mar/21 $${why}\:{the}\:{function}\:{cosz}\:{and}\:{sinz}\:{it}\:{is}\: \\ $$$${not}\:{bounded}\:{in}\:{complex}\:{number}\:? \\ $$ Answered by Olaf last updated on 03/Mar/21 $$\mathrm{cos}{z}\:=\:\mathrm{cos}\left({x}+{iy}\right) \\ $$$$\mathrm{cos}{z}\:=\:\mathrm{cos}{x}\mathrm{cos}\left({iy}\right)−\mathrm{sin}{x}\mathrm{sin}\left({iy}\right) \\…