Question

x- iy = 5+4i find the value of x square - y square (x,y belongs to R) {please explain }​

Answer 1

$\huge\mathcal\colorbox{lavender}{{\color{b}{✿Yøur-Añswer♡}}}$

$\large\bf{\underline{\red{VERIFIED✔}}}$

$\huge\mathcal\colorbox{lavender}{{\color{b}{✿Given♡}}}$

$x - iy = 5 + 4i$

$\huge\mathcal\colorbox{lavender}{{\color{b}{✿To- Find}}}$

$x² - y² [ x , y \: belongs \: to \: R ] .$

Used Concepts :-

• If two complex numbers are such that x + iy = a + ib .
• Then , we can equate their real and imaginary parts .

$\huge\mathcal\colorbox{lavender}{{\color{b}{✿Solution}}}$

$As , x - iy = 5 + 4i$

$=> x - yi = 5 + 4i$

${=> Equating \: real \: parts \: we \: get , }$

$=> x = 5$

${=> Equating \: imaginary \: parts \: we \: get , }$

$=> - y = 4$

$=> y = -4$

$Hence , \: The \: values \: of \: \: x \: and \: y \\ are \: 5 , -4 \: respectively \: and \\ they \: both \: belongs \: to \: R. \: So,$

$x² - y² :-$

$=> ( 5 )² - ( -4 )²$

$=> 25 - ( 16 )$

$=> 25 - 16 = 9$

$\huge\mathcal\colorbox{lavender}{{\color{b}{✿Final- Answer- is =9}}}$

Answer 2

ANSWER

Comparing the real & imaginary parts,

2x+3y=4--------------------------(1)

2y−3x=1----------------------------(2)

Solving eq(1)  &  eq(2),

4x+6y=8

−9x+6y=3

13x=5⇒x=135

y=1314