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Category: Algebra

find-all-a-b-R-such-that-1-a-bi-1-a-i-b-

Question Number 56183 by 121194 last updated on 11/Mar/19 $$\mathrm{find}\:\mathrm{all}\:{a},{b}\in\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}+{bi}}=\frac{\mathrm{1}}{{a}}+\frac{{i}}{{b}} \\ $$ Answered by kaivan.ahmadi last updated on 11/Mar/19 $$\frac{\mathrm{1}}{{a}+{bi}}=\frac{{b}+{ai}}{{ab}}\Rightarrow{ab}+\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right){i}−{ab}={ab}\Rightarrow \\…

Find-the-directional-derivatives-of-the-function-f-x-y-z-2x-2-3y-2-z-2-at-the-point-p-2-1-3-

Question Number 187255 by Spillover last updated on 15/Feb/23 $${Find}\:{the}\:{directional}\:{derivatives}\:{of}\:{the} \\ $$$${function}\: \\ $$$${f}\left({x},\mathrm{y},\mathrm{z}\right)=\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:{at}\:{the}\:{point}\:{p}\left(\mathrm{2},\mathrm{1},\mathrm{3}\right) \\ $$ Answered by MikeH last updated on…

what-is-the-cardinality-of-the-set-of-prime-numbers-whose-base-ten-digits-sums-up-to-10-

Question Number 187248 by MWSuSon last updated on 15/Feb/23 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{cardinality}\:\mathrm{of}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{whose} \\ $$$$\mathrm{base}\:\mathrm{ten}\:\mathrm{digits}\:\mathrm{sums}\:\mathrm{up}\:\mathrm{to}\:\mathrm{10} \\ $$ Commented by Frix last updated on 15/Feb/23 $$\mathrm{Same}\:\mathrm{as}\:\mathbb{N} \\ $$ Terms…

Find-x-if-x-4-a-x-0-lt-a-lt-2-9-

Question Number 187233 by ajfour last updated on 15/Feb/23 $${Find}\:{x}\:{if}\::\:\:\:{x}^{\mathrm{4}} +{a}={x}\:\:\:\:\forall\:\left(\mathrm{0}<{a}<\frac{\mathrm{2}}{\mathrm{9}}\right)\:\:\: \\ $$ Commented by MJS_new last updated on 15/Feb/23 $$\mathrm{maybe}\:\mathrm{off}\:\mathrm{topic}\:\mathrm{but}\:\mathrm{it}\:\mathrm{could}\:\mathrm{be}\:\mathrm{of}\:\mathrm{interest} \\ $$$$\left({x}−\frac{{p}^{\mathrm{2}} }{\mathrm{2}}−\frac{\sqrt{\mathrm{2}−{p}^{\mathrm{6}} }}{\mathrm{2}{p}}\right)\left({x}−\frac{{p}^{\mathrm{2}}…