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Category: Algebra

if-z-z-1-3-i-find-

Question Number 149142 by mathdanisur last updated on 03/Aug/21 $${if}\:\:\:{z}\:+\:\mid{z}\mid\:=\:\mathrm{1}\:+\:\sqrt{\mathrm{3}}\:\boldsymbol{{i}} \\ $$$${find}\:\:\:\boldsymbol{\varphi}\:=\:? \\ $$ Answered by liberty last updated on 03/Aug/21 $$\mathrm{z}=\mathrm{a}+\mathrm{b}{i} \\ $$$$\mid\mathrm{z}\mid=\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}}…

transform-the-ellipse-x-2-a-2-y-2-b-2-1-to-the-polar-equation-r-a-1-e-2-1-ecos-a-semimajor-axis-e-eccentricity-

Question Number 83590 by Tony Lin last updated on 04/Mar/20 $${transform}\:{the}\:{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:{to} \\ $$$${the}\:{polar}\:{equation}\:{r}=\:\frac{{a}\left(\mathrm{1}−{e}^{\mathrm{2}} \right)}{\mathrm{1}+{ecos}\theta} \\ $$$${a}:\:{semimajor}\:{axis} \\ $$$${e}:\:{eccentricity} \\ $$ Commented…

Question-18053

Question Number 18053 by mondodotto@gmail.com last updated on 14/Jul/17 Commented by prakash jain last updated on 14/Jul/17 $$\mathrm{can}\:\mathrm{u}\:\mathrm{please}\:\mathrm{type}\:\mathrm{question}?\:\mathrm{it}\:\mathrm{is}\:\mathrm{very} \\ $$$$\mathrm{difficult}\:\mathrm{to}\:\mathrm{read}\:\mathrm{image}. \\ $$ Commented by mondodotto@gmail.com…

Find-the-locus-of-a-point-which-moves-such-that-its-distance-from-the-line-y-4-is-a-constant-k-

Question Number 83570 by TawaTawa1 last updated on 03/Mar/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point}\:\mathrm{which}\:\mathrm{moves}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its} \\ $$$$\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{line}\:\:\:\mathrm{y}\:\:=\:\:\mathrm{4}\:\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\:\:\mathrm{k}. \\ $$ Commented by TawaTawa1 last updated on 03/Mar/20 $$\mathrm{Please}\:\mathrm{help}. \\ $$ Commented…

Question-83554

Question Number 83554 by Power last updated on 03/Mar/20 Answered by MJS last updated on 03/Mar/20 $${x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} −\mathrm{8}{x}+\frac{\mathrm{17}}{\mathrm{5}}=\mathrm{0} \\ $$$$\mathrm{let}\:{x}={t}−\mathrm{1} \\ $$$${t}^{\mathrm{4}} −\mathrm{6}{t}^{\mathrm{2}} +\frac{\mathrm{42}}{\mathrm{5}}=\mathrm{0}…