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vesna_86 [32]
3 years ago
5

Change the following percentage to fraction

"TexFormula1" title="116 \ \frac{2}{3} \%" alt="116 \ \frac{2}{3} \%" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
marta [7]3 years ago
3 0
I think the answer is 350/3
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If (3-4i) (x+yi) = 1 + 0i. The value of x and y is
Black_prince [1.1K]

Step-by-step explanation:

\textsf{\large{\underline{Solution}:}}

<h3><u>Given That:</u></h3>

\rm: \longmapsto (3 - 4i)(x + iy) = 1 + 0i

\rm: \longmapsto 3(x + iy)  - 4i(x + iy)= 1 + 0i

\rm: \longmapsto 3x + 3iy - 4ix +4y= 1 + 0i

<u>On rearranging the terms, we get:</u>

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<u>Comparing both sides, we get:</u>

\rm: \longmapsto 3x  + 4y = 1 --- (i)

\rm: \longmapsto 3y - 4x = 0 --- (ii)

<u>Multiplying (i) by 4, we get:</u>

\rm: \longmapsto 12x  + 16y = 4--- (iii)

<u>Multiplying (ii) by 3, we get:</u>

\rm: \longmapsto 9y - 12x = 0 --- (iv)

<u>Adding equations (iii) and (iv), we get:</u>

\rm: \longmapsto25y = 4

\rm: \longmapsto y =\dfrac{4}{25}

<u>From (ii), we get:</u>

\rm: \longmapsto 3y - 4x = 0

\rm: \longmapsto 3y  = 4x

\rm: \longmapsto x =  \dfrac{3}{4} y

\rm: \longmapsto x =  \dfrac{3}{4}  \times  \dfrac{4}{25}

\rm: \longmapsto x =  \dfrac{3}{25}

<u>Therefore:</u>

\rm: \longmapsto (x,y)= \bigg(  \dfrac{3}{25}, \dfrac{4}{25} \bigg)

★ <u>Which is our required answer.</u>

\textsf{\large{\underline{More To Know}:}}

\rm1.\  i^{4n} = 1

\rm2. \ i^{4n+1} = i

\rm3.\  i^{4n+2} = -1

\rm4.\ i^{4n+3} = -i

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