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By G. P. McKeown
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Extra info for Mathematics for Computing
13. If P represents the complex number IX = a +ib, then r = IIXI and = tan -1 (b/a). The angle is called the argument of IX, written arg(IX}, where arg(lX} is such that O~arg(IX}<21l:. ) Alternatively, if P is given in polar coordinates as (r, e) then P represents the complex number r cos e+ ir sin e= r(cos e+ i sin e}. 13 In polar coordinates, P is represented by (r, e) expression cos e+ i sin e occurs so commonly in this context that it is often written simply as cis e. Similarly, sic e= sin e+ i cos e.
If OF represents lX=a+ib and represents /3=c+id then OR represents 1X+/3=(a+c}+i(b+d}. The point P=(a, b} representing the complex number a+ib can also be defined using polar coordinates. 13. If P represents the complex number IX = a +ib, then r = IIXI and = tan -1 (b/a). The angle is called the argument of IX, written arg(IX}, where arg(lX} is such that O~arg(IX}<21l:. ) Alternatively, if P is given in polar coordinates as (r, e) then P represents the complex number r cos e+ ir sin e= r(cos e+ i sin e}.
4 If aE t6' is a root of the polynomial equation f(x) = 0, then the complex conjugate of a is also a root of the equation. 11 The Argand diagram The Argand Diagram The complex number a+ib can be represented as an ordered pair (a, b) of real numbers. This means that a complex number can be represented as a point in a plane. 11). If P is a point in the Argand diagram representing a complex number IX, then the directed line (or vector) & can also be used to represent IX. 12. If OF represents lX=a+ib and represents /3=c+id then OR represents 1X+/3=(a+c}+i(b+d}.