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Category: Algebra

find-the-value-of-1-1-1-1-i-1-i-1-i-pls-help-

Question Number 51922 by aseerimad last updated on 01/Jan/19 $${find}\:{the}\:{value}\:{of}… \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\frac{{i}}{\mathrm{1}+\frac{{i}}{\mathrm{1}+{i}}}}} \\ $$$${pls}\:{help}. \\ $$ Answered by ajfour last updated on 01/Jan/19 $$\mathrm{1}+\frac{{i}}{\mathrm{1}+{i}}\:=\:\mathrm{1}+\frac{{i}\left(\mathrm{1}−{i}\right)}{\mathrm{2}}\:=\:\frac{\mathrm{3}+{i}}{\mathrm{2}} \\…

Question-182973

Question Number 182973 by HeferH last updated on 17/Dec/22 Answered by Rasheed.Sindhi last updated on 18/Dec/22 $${x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0}\:;\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{27}} {\Sigma}}\left({x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }\right)^{\mathrm{2}} =? \\ $$$$\left({x}^{{n}}…

If-a-lt-b-lt-0-then-a-b-a-b-ab-

Question Number 182947 by myint last updated on 17/Dec/22 $$\mathrm{If}\:\:\mathrm{a}<\:\mathrm{b}<\mathrm{0},\:\:\mathrm{then}\:\:\mid\mathrm{a}−\mathrm{b}\mid\:+\:\mid\mathrm{a}+\mathrm{b}\mid\:+\:\mid\mathrm{ab}\mid= \\ $$ Commented by mr W last updated on 17/Dec/22 $$\neq{constant}\:{value}! \\ $$$${could}\:{be}\:{any}\:{positive}\:{value}! \\ $$…

If-ax-2-bx-c-i-0-has-purely-imaginary-roots-where-a-b-c-are-non-zero-real-answer-given-a-b-2-c-I-think-question-is-wrong-since-if-z-1-and-z-2-are-roots-than-z-1-z-2-b-a-purely-imaginary-pu

Question Number 51843 by prakash jain last updated on 31/Dec/18 $${If}\:{ax}^{\mathrm{2}} +{bx}+{c}+{i}=\mathrm{0}\:\mathrm{has}\:\mathrm{purely} \\ $$$$\mathrm{imaginary}\:\mathrm{roots}\:\mathrm{where}\: \\ $$$${a},{b},{c}\:{are}\:{non}−{zero}\:{real}. \\ $$$${answer}\:{given}:\:{a}={b}^{\mathrm{2}} {c} \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{question}\:\mathrm{is}\:\mathrm{wrong} \\ $$$$\mathrm{since}\:\mathrm{if}\:{z}_{\mathrm{1}}…

Determine-the-values-of-b-so-that-the-system-of-linear-equations-x-2y-z-1-2x-by-2z-2-4x-8y-b-2-z-2b-has-a-no-solution-b-a-unique-solution-c-infinitely-many-solutions-

Question Number 182900 by greougoury555 last updated on 16/Dec/22 $$\:{Determine}\:{the}\:{values}\:{of}\:{b}\:{so}\:{that} \\ $$$$\:{the}\:{system}\:{of}\:{linear}\:{equations} \\ $$$$\:\begin{cases}{{x}+\mathrm{2}{y}+{z}=\mathrm{1}}\\{\mathrm{2}{x}+{by}+\mathrm{2}{z}=\mathrm{2}}\\{\mathrm{4}{x}+\mathrm{8}{y}+{b}^{\mathrm{2}} \:{z}=\mathrm{2}{b}}\end{cases} \\ $$$$\:{has}\:\left({a}\right)\:{no}\:{solution}\: \\ $$$$\:\left({b}\right)\:{a}\:{unique}\:{solution} \\ $$$$\:\left({c}\right)\:{infinitely}\:{many}\:{solutions} \\ $$ Answered by…