If x-i y-3-5 i-7-6 i- then y-A- 9-85-B- -9-85C- 53-85D- none of these

The correct option is C 53/85 x+iy=3+5i/7 6i ⇒ x+iy=3+5i/7 6i×7+6i/7+6i ⇒ x+iy=21+53i+30i^2/49 36i^2 ⇒ x+iy=21 30+53i/49+36 ⇒ x+iy= 9/85+i53/85 On comparing bo ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Purely Imaginary

If x+i y=3+5 ...

Question

$If x + i y = \frac{3 + 5 i}{7 - 6 i}, then y=$

$\frac{9}{85}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$- \frac{9}{85}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{53}{85}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$\frac{53}{85}$

$x + i y = \frac{3 + 5 i}{7 - 6 i} \Rightarrow x + i y = \frac{3 + 5 i}{7 - 6 i} \times \frac{7 + 6 i}{7 + 6 i} \Rightarrow x + i y = \frac{21 + 53 i + 30 i^{2}}{49 - 36 i^{2}} \Rightarrow x + i y = \frac{21 - 30 + 53 i}{49 + 36} \Rightarrow x + i y = \frac{- 9}{85} + i \frac{53}{85}$

On comparing both the sides :

$y = \frac{53}{85}$

Suggest Corrections

Similar questions

Q. If

x + i y = \frac{3 + 5 i}{7 - 6 i},

then y =
(a) 9/85
(b) −9/85
(c) 53/85
(d) none of these

Q. Find

x

and

y

(x + i y) (7 - 5 i) = 9 + 4 i

Q. Given that

x, y \in R

solve:
(a)

(x + 2 y) + i (2 x - 3 y) = 5 - 4 i

(b)

(x + i y) + (7 - 5 i) = 9 + 4 i

(c)

x^{2} - y^{2} - i (2 x + y) 2 i

Q. Let

{(- 2 - \frac{1}{3} i)}^{3} = \frac{x + i y}{27} (i = \sqrt{- 1})

, where

x

and

y

are real numbers, then

y - x

equals :

Q. If

\frac{x}{9} = \frac{y}{17},

then (x+9):(y+17) is:

Join BYJU'S Learning Program

If x+iy=3+5i7−6i, then y=

The correct option is C 5385 x+iy=3+5i7−6i⇒ x+iy=3+5i7−6i×7+6i7+6i⇒ x+iy=21+53i+30i249−36i2⇒ x+iy=21−30+53i49+36⇒ x+iy=−985+i5385 On comparing both the sides : y=5385

$If x + i y = \frac{3 + 5 i}{7 - 6 i}, then y=$