When working with polynomials that have real coefficients, complex roots always come in conjugate pairs, i.e. if $a + bi$ is a root of a polynomial, then $a - bi$ is also a root of the same polynomial.
This is because of the properties of the sum and product of a polynomial's roots, which are covered further in Topic 2. To summarize, if the coefficients are all real, the sum and product of the roots must be real. If there is a complex root, the only way for the polynomial to still have real coefficients is for its complex conjugate to also be a root.
For example, if we have the quadratic $x^2 + 1 = 0$:
A polynomial with real coefficients can only have an even number of complex roots, as they always come in conjugate pairs.
De Moivre's theorem is a result formalizing the properties of complex numbers when raised to a power. To derive it, we can start with a complex number in Euler form:
$$re^{i\theta}$$
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