Question Number 14587 by tawa tawa last updated on 02/Jun/17 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{64}\:=\:\mathrm{0}\:\:\mathrm{in}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{form}\:\:\mathrm{a}\:+\:\mathrm{jb}, \\ $$$$\mathrm{Where}\:\:\mathrm{a}\:\:\mathrm{and}\:\:\mathrm{b}\:\:\mathrm{are}\:\mathrm{real}. \\ $$ Answered by mrW1 last updated on 03/Jun/17 $${x}={r}\left(\mathrm{cos}\:\theta+{i}\:\mathrm{sin}\:\theta\right) \\…
Question Number 79731 by M±th+et£s last updated on 27/Jan/20 Commented by M±th+et£s last updated on 27/Jan/20 $${AH}:{HC}=\mathrm{4}:\mathrm{3} \\ $$$${BG}:{GC}=\mathrm{5}:\mathrm{9} \\ $$$${find}\:{AF}:{FB} \\ $$ Commented by…
Question Number 14011 by Ruth1 last updated on 26/May/17 $$\mathrm{simplify}:\:\:\frac{\mathrm{4}\:−\:\mathrm{j5}}{\mathrm{1}\:+\:\mathrm{j2}} \\ $$ Commented by tawa tawa last updated on 26/May/17 $$\mathrm{Multiply}\:\mathrm{by}\:\mathrm{the}\:\mathrm{conjugate}\:\mathrm{both}\:\mathrm{numerator}\:\mathrm{and}\:\mathrm{denominator} \\ $$$$\frac{\left(\mathrm{4}\:−\:\mathrm{j5}\right)}{\left(\mathrm{1}\:+\:\mathrm{j2}\right)}\:×\:\frac{\left(\mathrm{1}\:−\:\mathrm{j2}\right)}{\left(\mathrm{1}\:−\:\mathrm{j2}\right)} \\ $$$$=\:\frac{\mathrm{4}\:−\:\mathrm{j8}\:−\:\mathrm{j5}\:+\:\mathrm{10j}^{\mathrm{2}}…
Question Number 13982 by tawa tawa last updated on 26/May/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{z}^{\mathrm{2}} \:−\:\mathrm{8}\left(\mathrm{1}\:−\:\mathrm{i}\right)\mathrm{z}\:+\:\mathrm{63}\:−\:\mathrm{16i}\:=\:\mathrm{0} \\ $$ Answered by ajfour last updated on 26/May/17 $${let}\:{z}={x}+{iy} \\…
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Question Number 13942 by FilupS last updated on 25/May/17 $$\mathrm{for}\:\:\boldsymbol{{v}}=\begin{bmatrix}{{y}}\\{{x}}\end{bmatrix},\:\:\:\:\boldsymbol{{v}}\in\mathbb{R}^{\mathrm{2}} \\ $$$$\boldsymbol{{v}}\:\mathrm{has}\:\mathrm{basis}\:\mathrm{vectors}\:\hat {{i}}\:\mathrm{and}\:\hat {{j}} \\ $$$$\: \\ $$$$\mathrm{Assume}\:\mathrm{we}\:\mathrm{apply}\:\mathrm{a}\:\mathrm{basis}\:\mathrm{transform}\:\mathrm{to} \\ $$$$\mathrm{obtain}\:\mathrm{new}\:\mathrm{basis}\:\mathrm{vectors}\:\hat {{i}}'\:\mathrm{and}\:\hat {{j}}' \\ $$$$\: \\…
Question Number 79308 by M±th+et£s last updated on 24/Jan/20 Commented by mr W last updated on 24/Jan/20 $${does}\:{this}\:{help}: \\ $$ Commented by mr W last…
Question Number 79131 by mathocean1 last updated on 23/Jan/20 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points}\:\mathrm{M}\: \\ $$$$\mathrm{such}\:\mathrm{as}\:\mid\mid\mathrm{M}\overset{\rightarrow} {\mathrm{A}}+\mathrm{M}\overset{\rightarrow} {\mathrm{B}}+\mathrm{2M}\overset{\rightarrow} {\mathrm{C}}\mid\mid=\mathrm{6}\sqrt{\mathrm{3}} \\ $$$$\mathrm{AB}=\mathrm{BC}=\mathrm{AC}=\mathrm{6} \\ $$$$\mathrm{ABC}\:\mathrm{is}\:\mathrm{triangle}. \\ $$ Commented by mathocean1 last…
Question Number 79121 by M±th+et£s last updated on 22/Jan/20 Answered by mr W last updated on 23/Jan/20 Commented by mr W last updated on 23/Jan/20…
Question Number 144166 by liberty last updated on 22/Jun/21 $$\mathrm{Given}\:\overset{\rightarrow} {\mathrm{p}}=\sqrt{\mathrm{2}}\:\hat {\mathrm{i}}+\mathrm{2}\sqrt{\mathrm{3}}\:\hat {\mathrm{j}}+\:\sqrt{\mathrm{3}}\:\hat {\mathrm{k}}\:\&\: \\ $$$$\:\overset{\rightarrow} {\mathrm{q}}=\mathrm{a}\:\hat {\mathrm{i}}+\hat {\mathrm{j}}\:+\mathrm{2}\hat {\mathrm{k}}\:.\:\mathrm{If}\:\mathrm{proj}_{\overset{\rightarrow} {\mathrm{q}}} \:\overset{\rightarrow} {\mathrm{p}}\:=\:\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{9}}\:\overset{\rightarrow} {\mathrm{q}}\: \\…