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write-1-i-23-3-i-13-in-re-i-

Question Number 132950 by mohammad17 last updated on 17/Feb/21 $${write}\:\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{23}} }{\left(\sqrt{\mathrm{3}}−{i}\right)^{\mathrm{13}} }\:{in}\left(\:{re}^{{i}\theta} \right) \\ $$ Answered by metamorfose last updated on 17/Feb/21 $${z}=\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{23}} }{\:\left(\sqrt{\mathrm{3}}−{i}\right)^{\mathrm{13}} }=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}}\:{e}^{{i}\frac{\mathrm{5}\pi}{\mathrm{12}}}…

Given-that-Z-0-1-2-all-integers-0-R-0-0-01-1-1-01-all-reals-0-Prove-that-R-gt-Z-

Question Number 1875 by Filup last updated on 20/Oct/15 $$\mathrm{Given}\:\mathrm{that}: \\ $$$${Z}=\left\{\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:…\right\}\:\mathrm{all}\:\mathrm{integers}\:\geqslant\mathrm{0} \\ $$$${R}=\left\{\mathrm{0},\:\mathrm{0}.\mathrm{01},\:…,\:\mathrm{1},\:\mathrm{1}.\mathrm{01},\:…\right\}\:\mathrm{all}\:\mathrm{reals}\:\geqslant\mathrm{0} \\ $$$$\:\mathrm{Prove}\:\mathrm{that}\:\mid{R}\mid>\mid{Z}\mid \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

proof-that-2-is-an-irrational-number-

Question Number 1865 by Denbang last updated on 18/Oct/15 $${proof}\:{that}\:\sqrt{\mathrm{2}}\:{is}\:{an}\:{irrational}\:{number} \\ $$$$ \\ $$ Answered by 123456 last updated on 18/Oct/15 $$\mathrm{suppuse}\:\mathrm{by}\:\mathrm{absurf}\:\mathrm{that}\:\sqrt{\mathrm{2}}\in\mathbb{Q},\:\mathrm{then} \\ $$$$\exists\left({p},{q}\right)\in\mathbb{Z},{q}\neq\mathrm{0}\:\mathrm{such}\:\mathrm{that}\:\sqrt{\mathrm{2}}=\frac{{p}}{{q}},\left({p},{q}\right)=\mathrm{1} \\…

Find-f-x-such-that-f-2x-f-x-

Question Number 132932 by bobhans last updated on 17/Feb/21 $${Find}\:{f}\left({x}\right)\:{such}\:{that}\:{f}\left(\mathrm{2}{x}\right)={f}\left({x}\right) \\ $$ Answered by Olaf last updated on 17/Feb/21 $${f}\left(\mathrm{2}{x}\right)\:=\:{f}\left({x}\right) \\ $$$$\Rightarrow\:{f}\left({x}\right)\:=\:{f}\left(\frac{{x}}{\mathrm{2}}\right)\:=\:{f}\left(\frac{{x}}{\mathrm{4}}\right)\:=\:…{f}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)… \\ $$$${f}\left({x}\right)\:=\:\underset{{n}\rightarrow\infty}…