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Advanced Math/Binomial Theorem applied to complex numbers

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Expert: Sherry Wallin - 11/3/2010


Question
I am having an issue using the binomial theorem to expand
and simplify this complex number. I have looked in my book,
but not even one example is given for this type of equation.

Use the Binomial Theorem to expand the complex number.
Simplify your result.
(2 − i)4

Answer
Page~

Here is the solution using the binomial theorem.

The binomial theorem says:

4C0*2^4*(-i)^0 + 4C1*2^3*(-i)^1 + 4C2*2^2*(-i)^2 + 4C3*2^1*(-i)^3 + 4C4*2^0*(-i)^4

= (4!/0!4!)*16*1 + (4!/1!3!)*8*(-i) + (4!/2!2!)*4*(-1) + (4!/3!1!)*2*i + (4!/4!0!)*1*1

= 1*16*1 - 4*8*i - 6*4 + 4*2*i + 1*1*1

= 16 - 32i - 24 + 8i + 1

= -7 - 24i


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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

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I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

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I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

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Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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