Question

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

Answer 1

Use the Binomial expansion ...

Explanation:

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: `1,5,10,10,5,1`

`(1-i)^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`

hope that helped