Question

.....

Answer 1

find the real values of x and y for which the complex numbers-3 +ix^2y and
x^2+y+4i are conjugate of each other

Answer 2

Hint :-
consider two equation
\(-3+i x^2y=x^2+y-4i\)
\(x^2+y+4i=-3-ix^2y\)

Answer 3

They are the same thing

Answer 4

I think there was a typo in the question
http://www.wolframalpha.com/input/?i=solve+x%5E2%2By%3D-3%2C+x%5E2y%3D-4+in+reals

Answer 5

also u can do this trick
(i still don't know which one will solve it lol )
\((-3 +ix^2y)(x^2+y+4i )= (9-x^4y^2)=((x^2+y)^2-16))\)

Answer 6

what are the options @No.name

Answer 7

No options given but the answer is
x=1, y= -4

x=-1
y=-4

Answer 8

\(−3+ix^2y=x^2+y−4i \)
means that
\(x^2+y=-3\)
\(x^2y=-4\)

Answer 9

for
\(x^2y=-4\) since you wanna real
then
\(x =2,\sqrt2 ,1\)
y=-1,-2,-4

try to find wich pair satisfy first equation
\((2,-1) (\sqrt 2 , -2) (1,-4) \)

Answer 10

so basically is it trial and error

Answer 11

also take negative side , it works

Answer 12

basicly you need to know the proposition
if C1,c2 both complex number
\(C_1=x_1+iy_1\)
\(C_2=x_2+iy_2\)

then \(C_1 = C_2\iff x_1=x_2 \text{ and } y_1=y_2\)

Answer 13

and you need to know how to construct conjugate of complex number ..

Answer 14

x^2 y = -4

x^2 +y = -3

I got these two equations then what i should do

Answer 15

ok , when you got x^2 y = -4
factorize -4

Answer 16

or solve like equation
x^2=-3-y
and
x^2=-4/y

Answer 17

or you can solve them by substitution :
x^2y = -4

y = -4/x^2

substitute this in second equation and solve x

Answer 18

Yessssss , got the answer , couldn't reply because of slow internet

Answer 19

In the second equation we would have to substitute that then again substitute
x^2 with a variable

Answer 20

exactly !

x^2 +y = -3
x^2 -4/x^2 = -3

t^2 +3t - 4 = 0
(t+4)(t-1) = 0

t = 1 or -4

discard -4

Answer 21

Even i substituted the same variable "t" (although it dosen't matter)
hehe gone are the days to substitute x's and y's

Answer 22

haha! so basically two complex numbers equal IF AND ONLY IF their real parts are equal, and their imaginary parts are equal

Answer 23

i think @ikram002p said that earlier..

Answer 24

yes