Question

find all complex numbers z such that z^2 = 7 - 24i

give your answer in the form a+bi

Answer 1

(a+bi)(a+bi)=7-24i
a^2+2abi-b^2=7-24i
now identify real and imaginary parts:
a^2-b^2=7
2ab=-24
and solve this system for a and b

Answer 2

apparently im only supposed to get values of -4 and 4 for a...i get something different

Answer 3

because first i isolate for b = -12/a
then i get 7 = (a-(12/a))(a+(12/a))

Answer 4

a=-12/b
substitute in 1º equation:
144/b^2-b^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+7x-144=0
solve this

Answer 5

x = -16, 9

Answer 6

b^2 = -16
b^2 = 9
cant take b^2 = -16

Answer 7

so b = +/- 3

Answer 8

right

Answer 9

so:
b^2=9
b=+-3

Answer 10

ok, i got it now...plug +/- 3 in equation

Answer 11

thanks!

Answer 12

in a=-12/b

Answer 13

yw