# How do you simplify 5-[(-3i+4)-2i]?

Jun 23, 2016

$5 - \left[\left(- 3 i + 4\right) - 2 i\right] = 1 + 5 i$

#### Explanation:

$5 - \left[\left(- 3 i + 4\right) - 2 i\right]$

= $5 - \left[- 3 i + 4 - 2 i\right]$

= $5 - \left[- 5 i + 4\right]$

Now we have a negative sign outside brackets.

How do we interpret it?

There are two ways

(i) it is as if we are multiplying by $- 1$ and hence

$- \left[- 5 i + 4\right] = - 1 \times \left[- 5 i + 4\right]$

= $\left(- 1\right) \times \left(- 5 i\right) + \left(- 1\right) \times 4 = 5 i - 4$ or

(ii) using simple properties of negative numbers i.e. negative of a negative is positive and negative of a positive is negative and hence again $- \left\{- 5 i + 4\right] = 5 i - 4$.

In any case, it means we change all the signs inside the brackets and above is equal to

$5 + 5 i - 4$

= $1 + 5 i$