iop360
find all complex numbers z such that z^2 = 7  24i
give your answer in the form a+bi



This Question is Closed

iop360
Best Response
You've already chosen the best response.
0
dw:1353792413116:dw

myko
Best Response
You've already chosen the best response.
1
(a+bi)(a+bi)=724i
a^2+2abib^2=724i
now identify real and imaginary parts:
a^2b^2=7
2ab=24
and solve this system for a and b

iop360
Best Response
You've already chosen the best response.
0
apparently im only supposed to get values of 4 and 4 for a...i get something different

iop360
Best Response
You've already chosen the best response.
0
because first i isolate for b = 12/a
then i get 7 = (a(12/a))(a+(12/a))

myko
Best Response
You've already chosen the best response.
1
a=12/b
substitute in 1º equation:
144/b^2b^2=7
144/b^2=7+b^2
144=7b^2+b^4
new variable: b^2=x
144=7x+x^2 or x^2+7x144=0
solve this

iop360
Best Response
You've already chosen the best response.
0
x = 16, 9

iop360
Best Response
You've already chosen the best response.
0
b^2 = 16
b^2 = 9
cant take b^2 = 16

iop360
Best Response
You've already chosen the best response.
0
so b = +/ 3

myko
Best Response
You've already chosen the best response.
1
right

myko
Best Response
You've already chosen the best response.
1
so:
b^2=9
b=+3

iop360
Best Response
You've already chosen the best response.
0
ok, i got it now...plug +/ 3 in equation

iop360
Best Response
You've already chosen the best response.
0
thanks!

myko
Best Response
You've already chosen the best response.
1
in a=12/b

myko
Best Response
You've already chosen the best response.
1
yw