QuestionDecember 25, 2025

4. Evaluate the expression. (8+9i)+(-5+4i) 5. Simplify the expression. 2i(7-i) A) 2+14i B) -2+14i C) 14-2i D) 14+2i 6. Evaluate the expression. (8-9i)(-5+6i) 7. Solve the quadratic equation by the square root method. x^2=144

4. Evaluate the expression. (8+9i)+(-5+4i) 5. Simplify the expression. 2i(7-i) A) 2+14i B) -2+14i C) 14-2i D) 14+2i 6. Evaluate the expression. (8-9i)(-5+6i) 7. Solve the quadratic equation by the square root method. x^2=144
4. Evaluate the expression. (8+9i)+(-5+4i) 5. Simplify the expression. 2i(7-i) A) 2+14i B) -2+14i C) 14-2i D) 14+2i 6. Evaluate the expression. (8-9i)(-5+6i) 7. Solve the quadratic equation by the square root method. x^2=144

Solution
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Answer

3+13i; D) 14+2i; 14+93i; x = 12,\ -12 Explanation 1. Add complex numbers (8+9i)+(-5+4i) = (8-5) + (9i+4i) = 3+13i 2. Distribute 2i over (7-i) 2i(7-i) = 2i \cdot 7 - 2i \cdot i = 14i - 2i^2. Since i^2 = -1, -2i^2 = -2(-1) = 2. So, 14i + 2. 3. Multiply complex numbers (8-9i)(-5+6i) = 8 \cdot -5 + 8 \cdot 6i - 9i \cdot -5 - 9i \cdot 6i = -40 + 48i + 45i -54i^2. -54i^2 = 54, so combine: -40+54=14, 48i+45i=93i. Result: 14+93i. 4. Solve x^2=144 by square root method Take square roots: x = \pm\sqrt{144} = \pm12.

Explanation

1. Add complex numbers<br /> $(8+9i)+(-5+4i) = (8-5) + (9i+4i) = 3+13i$<br />2. Distribute $2i$ over $(7-i)$<br /> $2i(7-i) = 2i \cdot 7 - 2i \cdot i = 14i - 2i^2$. Since $i^2 = -1$, $-2i^2 = -2(-1) = 2$. So, $14i + 2$.<br />3. Multiply complex numbers<br /> $(8-9i)(-5+6i) = 8 \cdot -5 + 8 \cdot 6i - 9i \cdot -5 - 9i \cdot 6i = -40 + 48i + 45i -54i^2$. $-54i^2 = 54$, so combine: $-40+54=14$, $48i+45i=93i$. Result: $14+93i$.<br />4. Solve $x^2=144$ by square root method<br /> Take square roots: $x = \pm\sqrt{144} = \pm12$.
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