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

Jan 21, 2016

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: $1 , 5 , 10 , 10 , 5 , 1$

${\left(1 - i\right)}^{5} = \left(1\right) {\left(- i\right)}^{5} + \left(5\right) {\left(- i\right)}^{4} + \left(10\right) {\left(- i\right)}^{3} + \left(10\right) {\left(- i\right)}^{2} + \left(5\right) {\left(- i\right)}^{1} + \left(1\right) {\left(- i\right)}^{0}$

$= 1 \left(- i\right) + 5 \left(1\right) + 10 \left(i\right) + 10 \left(- 1\right) + 5 \left(- i\right) + 1 \left(1\right)$

$= - 4 + 4 i$

hope that helped