Performing Arithmetic with Complex Numbers

We can simplify the given expression by combining like terms. Recall the definition of the imaginary unit

i .

- 1 = i and - 1 = i^{2}

Let's begin by rewriting the roots that have a negative radicand as imaginary numbers.

3 - 24 \cdot 2 - 18

Simplify

SplitIntoFactorsSplit into factors

3 - 1 \cdot 24 \cdot 2 - 1 \cdot 18

a \cdot b = a \cdot b

3 - 1 \cdot 24 \cdot 2 - 1 \cdot 18

- 1 = i

3 i \cdot 24 \cdot 2 i 18

CommutativePropAddCommutative Property of Addition

3 \cdot 2 \cdot i \cdot i \cdot 24 \cdot 18

6 i^{2} \cdot 24 \cdot 18

i^{2} = - 1

6 (- 1) \cdot 24 \cdot 18

a (- b) = - a \cdot b

- 6 \cdot 24 \cdot 18

a \cdot b = a \cdot b

- 6 \cdot 24 \cdot 18

- 6 \cdot 432

Now we can simplify the square root.

- 6 \cdot 432

RewriteRewrite

432

as

144 \cdot 3

- 6 \cdot 144 \cdot 3

a \cdot b = a \cdot b

- 6 \cdot 144 \cdot 3

CalcRootCalculate root

- 6 \cdot 12 \cdot 3

- 723

Performing Arithmetic with Complex Numbers 1.19 - Solution