Yahami
Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

If (3-4i) (x+yi) = 1 + 0i. The value of x and y is
(a). (3/25,4/25)
(b). (1/6,0)
(c). (1,1)
(d). (0.5)​

If 34i Xyi 1 0i The Value Of X And Y Isa 325425b 160c 11d 05 class=

Sagot :

SalmonWorldTopper

Step-by-step explanation:

[tex]\textsf{\large{\underline{Solution}:}}[/tex]

Given That:

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

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

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

On rearranging the terms, we get:

[tex] \rm: \longmapsto (3x + 4y)+ (3y - 4x)i = 1 + 0i[/tex]

Comparing both sides, we get:

[tex] \rm: \longmapsto 3x + 4y = 1 --- (i)[/tex]

[tex] \rm: \longmapsto 3y - 4x = 0 --- (ii)[/tex]

Multiplying (i) by 4, we get:

[tex] \rm: \longmapsto 12x + 16y = 4--- (iii)[/tex]

Multiplying (ii) by 3, we get:

[tex] \rm: \longmapsto 9y - 12x = 0 --- (iv)[/tex]

Adding equations (iii) and (iv), we get:

[tex] \rm: \longmapsto25y = 4[/tex]

[tex] \rm: \longmapsto y =\dfrac{4}{25} [/tex]

From (ii), we get:

[tex] \rm: \longmapsto 3y - 4x = 0 [/tex]

[tex] \rm: \longmapsto 3y = 4x [/tex]

[tex] \rm: \longmapsto x = \dfrac{3}{4} y[/tex]

[tex] \rm: \longmapsto x = \dfrac{3}{4} \times \dfrac{4}{25} [/tex]

[tex] \rm: \longmapsto x = \dfrac{3}{25} [/tex]

Therefore:

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

★ Which is our required answer.

[tex]\textsf{\large{\underline{More To Know}:}}[/tex]

[tex]\rm1.\ i^{4n} = 1[/tex]

[tex]\rm2. \ i^{4n+1} = i[/tex]

[tex]\rm3.\ i^{4n+2} = -1[/tex]

[tex]\rm4.\ i^{4n+3} = -i[/tex]

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.