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Unformatted text preview: SUCET, PSHSNCE, and other entrance tests.
where a, b – real numbers, i – an imaginary unit.
In more details about complex numbers see the section “Complex numbers”.
E x a m p l e s of complex numbers: 3 + 4 i , 7 – 13.6 i , 0 + 25 i = 25 i , 2 + i. Monomials and polynomials
Monomial is a product of two or some factors, each of them is either a number, or a letter, or a power of a letter.
For example,
3 a 2b 4, bd3, – 17 a b c are monomials. A single number or a single letter may be also considered as a monomial. Any factor of a
monomial may be called a coefficient. Often only a numerical factor is called a coefficient. Monomials are
called similar or like ones, if they are identical or differed only by coefficients. Therefore, if two or some
monomials have identical letters or their powers, they are also similar (like) ones. Degree of monomial is a sum
of exponents of the powers of all its letters.
Addition of monomials. If among a sum of monomials there are similar ones, he sum can be reduced to the
more simple form:
ax3y2 –5b3x3y2+c5x3y2=(a–5b3+c5)x3y2.
This operation is called reducing of like terms. Operation, done here, is called also taking out of brackets.
Multiplication of monomials. A product of some monomials can be simplified, only if it has powers of the
same letters or numerical coefficients. In this case exponents of the powers are added and numerical coefficients
are multiplied.
Example:
5 a x 3 z 8 ( – 7 a 3 x 3 y 2 ) = – 35 a 4 x 6 y 2 z 8 . Math I  20  Feel free to pass this on to your friends, but please don’t post it online.
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This note was uploaded on 07/21/2013 for the course UPCAT 2014 taught by Professor Otis during the Spring '13 term at University of the Philippines Diliman.
 Spring '13
 OTIS

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