Question

Complex numbers help!

if ( x + iy )² = 4i find all the real values of x and y

Answer 1

so, expand (x+iy)^2
can you ?

Answer 2

\[x ^{2} - y ^{2} + 2xyi = 4 i\]

Answer 3

correct

Answer 4

now whats the real part of that ?

Answer 5

x² - y²

Answer 6

yes,
and real part of right side =0 right ?
so equating the real parts, we get
x^2-y^2 =0
got this ?

Answer 7

ohhhh x² - y² = 0

Answer 8

yes

Answer 9

now equate the imaginary part too

Answer 10

2xyi = 4i

Answer 11

so 2xy = 4
right ?

Answer 12

yea but there is only two variables i've been struggling with this for a half an hour

Answer 13

we have 2 equations and 2 variables
so we can find them easily

Answer 14

x^2-y^2 = 0
what do you get from this ?