How do you write this expression in the standard form a+bi given (1−i)5?

veceriraby

veceriraby

Answered

2022-02-02

How do you write this expression in the standard form a+bi given (1i)5?

Answer & Explanation

oferenteoo

oferenteoo

Expert

2022-02-03Added 12 answers

Step 1
Since any exponent on the first term of 1 is simply 1, we can ignore that term.
Pay attention to the second term -i and the exponents on that term from the Binomial expansion plus use the Pascal triangle coefficients: 1, 2, 10, 10, 5, 1
(1i)5=(1)(i)5+(5)(i)4+(10)(i)3+(10)(i)2+(5)(i)1+(1)(i)0
=1(i)+5(1)+10(i)+10(1)+5(i)+1(1)
=4+4i

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