Multiplying Complex Numbers

Multiplying complex numbers is very similar to multiplying in the real number system. The exponent rules will be used as well as the distributive property. There will be one additional step where the imaginary components with exponents will be replaced with its simplest form.

Quick Review:
i

-1

i With exponents

Simplest form

i2 -1
i3 -i
i4 1


  • Multiplying monomials


(3i)(-4i) (-4i2)(5i) Exponent Rule

= -12 i2 = -20 i3   x a x b = x a+b

= -12 (-1)= -20 (-i)

= 12   = 20i

  • Multiply a polynomial by a monomial


4i(2i2 - 3i + 7)


= 4i(2i2 - 3i + 7) Use the distributive property

= 8i3 - 12i2 + 28i

= 8(-i) - 12 (-1) + 28i replace the imaginary numbers with exponents to the      simplest form

= -8i + 12 + 28i simplify

= 12 + 20i combine like terms and write in a + bi form

  • Multiply a binomial by a binomial


(5+2i)(2 - 6i)

= 10 - 30i + 4i - 12i2FOIL or distributive property

= 10 - 26i - 12i2   combine like terms

= 10 - 26i - 12(-1)   replace the imaginary numbers with exponents to the   simplest form

= 22 -26i      combine like terms and write in a + bi form

(2 - 3i2)(2 + 3i2)

= 4 + 6i2 - 6i2 -9i4 FOIL or distributive property

= 4 - 9i4      combine like terms

= 4 - 9(1)    replace the imaginary numbers with exponents to the simplest form

= -5   combine like terms



Multiply Complex Numbers by using the rules for the real numbers then replace the imaginary number with exponents with its simplest form and simplify. When applicable make sure that the answer is in a + bi form.

Related Links:
Math
algebra
Complex Numbers
Operations With Complex Numbers
Rationalizing Imaginary Denominators

Identifying Real and Imaginary Numbers Quiz
Adding Complex Numbers Quiz
Subtracting Complex Numbers Quiz
Multiplying Complex Numbers. Quiz
Dividing Complex Numbers Quiz
Mixed Complex Number. Quiz


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