A complex number $z$ is composed of two parts: $z=x+$yi$,$ where $x,$ a real number is known as the real part of $z$ and $y$ another real number is the imaginary part. The symbol i represents a square root of $-1.$

The negation of $z$ is $-z=-x-yi,$

The magnitude of $z$ is $|z|=\sqrt[\phantom{2}]{x^2+y^2}.$ The magnitude can be thought of as the distance a complex number $z$ lies from the origin of the complex plane

The arithmetic operations between two complex numbers $z1=x1+y1$i and $z2=x2+y2$i are defined as follows:

$z1+z2=(x1+x2)+(y1+y2)i,$

$z1-z2=(x1-x2)+(y1-y2)i,$

$z1**z2=(x1x2-y1y2)+(x1y2+x2y1)i,$

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