"One root of $\displaystyle x^4 - 3x^2 - 4 = 0$ is i. What are the other three roots?"
How do I do this with i?
If someone could briefly walk me through this, that'd be awesome. Thanks.
Hi Savior_Self,
Remember, if an imaginary number is a zero to the polynomial function, so is its conjugate.
Therefore, if i is a zero, then -i is a zero.
(x-i) and (x+i) are factors.
Multiply these two together to get $\displaystyle x^2+1$
Now, divide this into your original function to get $\displaystyle x^2-4$
If i is a factor, and -i is a factor and $\displaystyle x^2-4$ is a factor then $\displaystyle (x-i)(x+i)(x-2)(x+2)=0$
Your zeros are $\displaystyle \{i, -i, 2, -2\}$