Multiplying Complex Numbers
Quick Review:
i |
$\sqrt{-1}$ |
i With exponents |
Simplest form |
i^{2} | -1 |
i^{3} | -i |
i^{4} | 1 |
- Multiplying monomials
(3i)(-4i) (-4i^{2})(5i) Exponent Rule
= -12 i^{2} = -20 i^{3} ${x}^{a}\u2022{x}^{b}={x}^{a+b}$
= -12 (-1)= -20 (-i)
= 12 = 20i
- Multiply a polynomial by a monomial
4i(2i^{2} - 3i + 7)
= 4i(2i^{2} - 3i + 7) Use the distributive property
= 8i^{3} - 12i^{2} + 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 - 12i^{2}FOIL or distributive property
= 10 - 26i - 12i^{2} 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
= 10 - 30i + 4i - 12i^{2}FOIL or distributive property
= 10 - 26i - 12i^{2} 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 - 3i^{2})(2 + 3i^{2})
= 4 + 6i^{2} - 6i^{2} -9i^{4} FOIL or distributive property
= 4 - 9i^{4} combine like terms
= 4 - 9(1) replace the imaginary numbers with exponents to the simplest form
= -5 combine like terms
= 4 + 6i^{2} - 6i^{2} -9i^{4} FOIL or distributive property
= 4 - 9i^{4} 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.
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