Yahami
Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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 appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.