Easy question (1 Viewer)

[sasquatch]

Theres a question im doing.. well i think ive done it but im not sure if my steps are right.. i forgot everything practically bout complex numbers.. and so can somebody do this question with full working out please:

Find z in z⁴ - 2z² + 9 = 0.

 

[_ShiFTy_]

Let X = z^2
Then use the quadratic formula

 

[Raginsheep]

to make it easier to see, let z^2=u
thus u get: u^2 -2u+9=0
use quadratic formula to solve for u giving you two answers
u=blah,
u=another blah
thus, z^2=blah,
z^2=another blah
root both sides to get z.

 

[sasquatch]

mehh... thats not the part i was confused about... seems people cant be bothered to help hehe.. i dont blame yuo though...erm what i was stuffed about is the square rooty things..erm..

i had z = +/- root(1 +/- i root2)

and yeah thats what i was stuck on..

 

[Raginsheep]

Umm......im not sure whether that's entirely correct or whatever but if you get z=something, then thats the answer you're looking for...

 

[sasquatch]

no no ah....................... man i know all that!!! what i want to see demonstrated is the writing of the roots without the square root symbols. Like equating a + ib = Root(something + i*something) and then you square both sides, ect.

 

[Riviet]

You're actually finding the square root of 1+i.sqrt8. Let (a+ib)²=1+i.sqrt8, and expand LHS, equate real and imaginary parts, solve the equations simultaneously, find a and b, and substitute into a+ib. You will need to find the square root of 1+i.sqrt8 and 1-i.sqrt8 separately.

 

[sasquatch]

oh ok cool..thats what i was looking for..thanks!