Question

Find a and b if (a+bi)^2=12+16i. I don't know what to do?

Answer 1

I have expanded and got:
\[ab=8\] and \[a^2-b^2=12\]

Answer 2

ab =8
so
a=8/b

plug this in
a^2-b^2 =12
and you will get an equation only in a

Answer 3

I need to find the real and imaginary value

Answer 4

(8/b)^2 - b^2 =12

64 - b^4 = 12b^2

take b^2 = x

x^2 +12x-64 =0
solve this quadratic to get b^2

Answer 5

Then I can square root that answer to get b, put that in the ab=8 to get the a value, right?

Answer 6

there's an alternative way too, if you know how to convert complex no. from cartesian to polar co-ordinates

Answer 7

Nope, don't know that way

Answer 8

ok, so go with
"Then I can square root that answer to get b, put that in the ab=8 to get the a value, right?"

yes thats right

Answer 9

Great. But what is the real and imaginary number? I only get A and B that way, not real and imaginary.

Answer 10

"Find a and b "

you want a and b only

Answer 11

Sorry, wrote the question wrong. I want to find the real and imaginary number. I guessed that was the A and B value, right?

Answer 12

'the real and imaginary number' of what ?
Post the exact question you were asked...

Answer 13

'(a+bi)^2=12+16i , find the real and imaginary number'
this does not make sense

Answer 14

K: Find the real numbers \[a\] and \[b\] if \[(a+bi)^2=12+16i\]

Answer 15

YES, a and b are both real numbers

Answer 16

"bi" is an imaginary number

Answer 17

and
'a+bi' is a complex number

Answer 18

OH, Now I get it. Thanks (sorry for being bothersome)

Answer 19

no problem :)
welcome ^_^