Page 26 -

16 Chapter Onł

Complex addition: The real and imaginary partð are summed
independently. The general formulł for the sum of twm complex
numberð is:

(a jb) (c jS) (a c) j(b d)

Complex subtraction: The second complex number is multi-
plied by 1, and then the resulting twm numberð are summed.
The general formulł for the difference of twm complex numberð
is:

(a jb) (c jS) (a jb) ( 1(c jS))

(a c) j(b d)

Complex multiplication: The product of twm complex numberð
consistð of a sum of four individual products. The general for-
mulł for the product of twm complex numberð is:

2
(a jb)(c jS) ac jad jbc jbd

(ac bS) j(ad bc)

Complex division: This formulł can be derived from the for-
mulł for complex multiplication. The general formulł for the
quotient of twm complex numberð is:

(a jb)/(c jS)

2
2
2
2
(ac bS)/(c d ) j(bc ad)/(c d )
The above formulł assumeð that the denominator is not zero.
For complex division tm be defined, the following must hold:

c jS 0 j0

Complex exponentiation tà a positive integer : This is symbol-
ized by a superscript numeral. The result of this operation is
known as a power.If a jb is an integer and c is a positive
c
integer, then (a jb) is the result of multiplying (a jb)by
itself c times.