Question Number 51320 by Tawa1 last updated on 25/Dec/18 $$\mathrm{The}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\:\mathrm{represent}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{numbers}\:\:\mathrm{z}_{\mathrm{1}} ,\:\mathrm{z}_{\mathrm{2}} ,\:\mathrm{z}_{\mathrm{3}} \: \\ $$$$\mathrm{respectively}.\:\mathrm{And}\:\mathrm{G}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{A}\:\mathrm{B}\:\mathrm{C},\:\:\mathrm{if} \\ $$$$\mathrm{4z}_{\mathrm{1}} \:+\:\mathrm{z}_{\mathrm{2}} \:+\:\mathrm{z}_{\mathrm{3}} \:\:=\:\:\mathrm{0},\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mid}\:\mathrm{point}\:\mathrm{of}\:\:\mathrm{AG}. \\ $$ Answered by tanmay.chaudhury50@gmail.com…
Question Number 182394 by Tawa11 last updated on 08/Dec/22 Commented by Tawa11 last updated on 08/Dec/22 $$\mathrm{Number}\:\mathrm{18} \\ $$ Answered by CrispyXYZ last updated on…
Question Number 51316 by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18 Commented by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18 Commented by Cheyboy last updated on 26/Dec/18 $$\mathrm{Waaw}!!\:\mathrm{this}\:\mathrm{is}\:\mathrm{very}\:\:\mathrm{good}.\mathrm{thank} \\…
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Question Number 51307 by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18 Commented by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18 $${this}\:{is}\:{not}\:{question}\:{but}\:{may}\:{help}\:{others}… \\ $$ Commented by afachri last updated on…
Question Number 116822 by bemath last updated on 07/Oct/20 $$\:\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{{i}}\:=? \\ $$ Commented by Dwaipayan Shikari last updated on 07/Oct/20 $$\sqrt{{i}}=\left(\sqrt{\frac{\mathrm{2}{i}}{\mathrm{2}}}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\sqrt{\left(\mathrm{1}+\mathrm{2}{i}+{i}^{\mathrm{2}} \right)}=\pm\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\left(\mathrm{1}+{i}\right) \\ $$ Answered…
Question Number 51284 by Tawa1 last updated on 25/Dec/18 $$\mathrm{If}\:\:\boldsymbol{\mathrm{x}}\:\mathrm{is}\:\mathrm{real},\:\mathrm{show}\:\mathrm{that}\:\:\left(\mathrm{2}\:+\:\mathrm{j}\right)\mathrm{e}^{\left(\mathrm{1}\:+\:\mathrm{j3}\right)\boldsymbol{\mathrm{x}}} \:+\:\left(\mathrm{2}\:−\:\boldsymbol{\mathrm{j}}\right)\boldsymbol{\mathrm{e}}^{\left(\mathrm{1}\:−\:\boldsymbol{\mathrm{j}}\mathrm{3}\right)\boldsymbol{\mathrm{x}}} \\ $$$$\mathrm{is}\:\mathrm{also}\:\mathrm{real} \\ $$ Commented by maxmathsup by imad last updated on 25/Dec/18 $${first}\:{what}\:{mean}\:{j}\:{and}\:{j}\mathrm{3}?…
Question Number 51250 by Tawa1 last updated on 25/Dec/18 $$\mathrm{Given}\:\mathrm{that}\:\:\:\mathrm{z}_{\mathrm{1}} \:=\:\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{R}\:+\:\mathrm{j}\omega\mathrm{L}\:;\:\:\:\mathrm{z}_{\mathrm{2}} \:=\:\mathrm{R}_{\mathrm{2}} \:;\:\:\mathrm{z}_{\mathrm{3}} \:=\:\frac{\mathrm{1}}{\mathrm{j}\omega\mathrm{C}_{\mathrm{3}} } \\ $$$$\mathrm{and}\:\:\mathrm{z}_{\mathrm{4}} \:=\:\mathrm{R}_{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{j}\omega\mathrm{C}_{\mathrm{4}} }\:\:\mathrm{and}\:\mathrm{also}\:\mathrm{that}\:\:\:\mathrm{z}_{\mathrm{1}} \mathrm{z}_{\mathrm{3}} \:\:=\:\:\mathrm{z}_{\mathrm{2}} \mathrm{z}_{\mathrm{4}} \:,\:\:\:\mathrm{express}\:…
Question Number 51248 by Tawa1 last updated on 25/Dec/18 $$\mathrm{If}\:\:\:\:\:\frac{\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{j}\omega\mathrm{L}}{\mathrm{R}_{\mathrm{3}} }\:\:=\:\:\frac{\mathrm{R}_{\mathrm{2}} }{\mathrm{R}_{\mathrm{4}} \:−\:\mathrm{j}\:\frac{\mathrm{1}}{\omega\mathrm{C}}}\:\:,\:\:\:\mathrm{where}\:\:\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} ,\:\mathrm{R}_{\mathrm{3}} ,\:\mathrm{R}_{\mathrm{4}} ,\:\omega,\:\mathrm{L}\:\mathrm{and}\:\mathrm{C} \\ $$$$\mathrm{are}\:\mathrm{real}\:,\:\:\mathrm{show}\:\mathrm{that}\:\:\:\:\mathrm{L}\:=\:\frac{\mathrm{C}\:\mathrm{R}_{\mathrm{2}} \mathrm{R}_{\mathrm{3}} }{\omega^{\mathrm{2}} \mathrm{C}^{\mathrm{2}} \mathrm{R}_{\mathrm{4}} ^{\mathrm{2}}…