Question

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

Answer 1

Given :-

x - iy = 5 + 4i

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 .

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

Henceforth , Our Required Answer Is 9 .

Answer 2

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

$x - iy = 5 + 4i$

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

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

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

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

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

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

$=> x = 5$

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

$=> - y = 4$

$=> y = -4$

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

$x² - y² :-$

$=> ( 5 )² - ( -4 )²$

$=> 25 - ( 16 )$

$=> 25 - 16 = 9$

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

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