Here, using $z$ instead of $x$ means that the variable is complex. $w$ is also sometimes used.
The first step is to find the one real solution. Since it’s a cubic, there will be three solutions and by examining the graph you can see that there always must be at least one real solution (cubics always cross the $y$-axis at least once).
For $z = 1$:
$$ z^3 + 9z^2 + 33z + 25 1^3 + 9\times1^2 + 33\times1 + 25 \neq 0 $$
2020-09-03
1 min read
A complex number is a number with both a real and imaginary part.
See Also [[Further Maths - Polar Form]]S [[Further Maths - Argand Diagrams]]S [[Further Maths - Loci in the Argand Diagram]]S [[Further Maths - Regions in the Argand Diagram]]S [[Further Maths - Exponential Form of Complex Numbers]]S [[Further Maths - Trig Equations with Complex Numbers]]S [[Further Maths - Roots of Complex Numbers]]S Introducing $i$ First, a couple of definitions:
2020-09-03
5 min read