# How do you find the exact value of 2(3-i^14)-(5-i^23)?

##### 1 Answer
Apr 2, 2016

$3 - i$.

#### Explanation:

Remember that ${i}^{4} = 1$. So ${i}^{8} = {i}^{12} = {i}^{16} = \ldots = 1$. Then ${i}^{14} = \left({i}^{12}\right) \left({i}^{2}\right) = \left(1\right) \left(- 1\right) = - 1$.

Figure out ${i}^{23}$ similarly. Then simplify the expression as usual by adding all the real numbers together and adding all the imaginary numbers together. Remember, of course, that some of the numbers you're adding are negative.