Solve x² + 4x + 29 = 0. Plot the two roots on the Argand plane.

For $ax^2 + bx + c = 0$ with real coefficients and $D = b^2 - 4ac < 0$, the roots are $\dfrac{-b \pm i\sqrt{-D}}{2a}$, a conjugate pair. Their sum is $-\dfrac{b}{a}$ and their product is $\dfrac{c}{a}$. A square root $x + iy$ of $a + ib$ has $x^2 - y^2 = a$, $2xy = b$ and $x^2 + y^2 = \sqrt{a^2 + b^2}$.