Question

1. rewrite the expression: (3 + 6i)(7 - 2i)

1 point (c.cn.a.2)

1. solve the quadratic equation:

(3x - 2)² = -4(2x - 1)
1 point (a.rei.b.4)

Explanation:

Problem 4: Rewrite the expression \((3 + 6i)(7 - 2i)\)

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 \(i^2=-1\)

Recall that \(i^2 = - 1\), so substitute \(-1\) for \(i^2\) in the expression:

$$
LATEXBLOCK1
$$

Step 3: Combine like terms

Combine the real parts and the imaginary parts separately:

$$
LATEXBLOCK2
$$

Step 1: Expand both sides of the equation

First, expand \((3x - 2)^2\) using the formula \((a - b)^2=a^2-2ab + b^2\) where \(a = 3x\) and \(b = 2\), and expand \(-4(2x - 1)\) using the distributive property:

$$
LATEXBLOCK0
$$

Step 2: Move all terms to one side to form a standard quadratic equation

Subtract \(-8x + 4\) from both sides to get:

$$
LATEXBLOCK1
$$

Step 3: Factor out the greatest common factor (GCF)

The GCF of \(9x^2\) and \(-4x\) is \(x\), so factor out \(x\):

$$ x(9x - 4)=0 $$

Step 4: Use the zero - product property

If \(ab = 0\), then either \(a = 0\) or \(b = 0\). So we set each factor equal to zero and solve for \(x\):

• If \(x = 0\), then the equation is satisfied.
• If \(9x-4 = 0\), then \(9x=4\), and \(x=\frac{4}{9}\)

Answer:

\(33 + 36i\)

Problem 7: Solve the quadratic equation \((3x - 2)^2=-4(2x - 1)\)