Question

8 matching 3 points simplify and match each complex number. (2+3i)(4-2i) (2-i)(2+i) (5+i)(2-3i)

Explanation:

Simplifying \((2 + 3i)(4 - 2i)\)

Step 1: Use the distributive property (FOIL method)

Multiply each term in the first complex number by each term in the second complex number:

$$
LATEXBLOCK0
$$

Step 2: Simplify using \(i^2=-1\)

Combine like terms and substitute \(i^2 = - 1\):

$$
LATEXBLOCK1
$$

Simplifying \((2 - i)(2 + i)\)

Step 1: Recognize the difference of squares formula \((a - b)(a + b)=a^2 - b^2\)

Here, \(a = 2\) and \(b = i\), so:

$$ (2 - i)(2 + i)=2^2 - i^2 $$

Step 2: Simplify using \(i^2=-1\)

Substitute \(i^2=-1\) into the expression:

$$
LATEXBLOCK0
$$

Simplifying \((5 + i)(2 - 3i)\)

Step 1: Use the distributive property (FOIL method)

Multiply each term in the first complex number by each term in the second complex number:

$$
LATEXBLOCK0
$$

Step 2: Simplify using \(i^2=-1\)

Combine like terms and substitute \(i^2 = - 1\):

$$
LATEXBLOCK1
$$

Answer:

s:

• \((2 + 3i)(4 - 2i)=14 + 8i\)
• \((2 - i)(2 + i)=5\)
• \((5 + i)(2 - 3i)=13-13i\)