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the argand diagram
chapter 2 - the argand diagram
| Term | Definition |
|---|---|
| the complex plane | the z plane / argand diagram, how complex numbers are represented on a graph |
| plotting complex numbers | the real part of a complex number forms the equivalent of the x axis, and the imaginary part the y axis |
| the absolute value of a complex number | the distance from the origin, sqrt(a^2 + b^2) |
| the argument of z | the angle the number makes anti-clockwise from the positive real axis, generally arctan(b/a) but it depends on the quadrant the number is placed in |
| the modulos-argument form of a + bi | r[cos(theta) + isin(theta)] where r = |z| theta = arg(z) a = rcos(theta) b = rsin(theta) |
| multiplication of two complex numbers | |z1z2| = r1r2 arg(z1z2) = arg(z1) + arg(z2) |
| division of two complex numbers | |z1/z2| = r1/r2 arg(z1/z2) = arg(z1) - arg(z2) |
| formula for a circle in the complex plane | |z-(a+bi)| = r center (a,b), radius r |
| |z-z1| = |z-z2| | perpendicular bisect of the line formed between z1 to z2 |
| |z-z1| = r locus | a circle centred z1, radius r |
| |z-z1| = |z-z2| locus | the perpendicular bisector of the line formed between z1 and z2 |
| arg(z-z1) = theta locus | a half line, from z1, theta radians from the horizontal axis to the point anti-clockwise |
| half-line description | A line with a defined start that still tends towards an infinity as its length increases This means that, when doing the Cartesian equation, x and y will have to be bounded |
Created by:
That cool NAMe
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