Question

for this quiz, select the best answer from

you have 20 minutes to complete the quiz.

you have only one attempt.

question 1

\\((2 + 3i) - (-8 + i)\\)

• \\(-6 + 4i\\)
• \\(4i\\)
• \\(10 + 2i\\)
• \\(2i\\)

Explanation:

🆕 New Concept Discovered: Operations with Complex Numbers
Adding and subtracting real and imaginary parts.

Step 1: Distribute the negative sign

Distribute the subtraction sign to both terms inside the second set of parentheses:

$$ -( -8 + i ) = 8 - i $$

Rewrite the entire expression without parentheses:

$$ 2 + 3i + 8 - i $$

Step 2: Group and combine like terms

Group the real numbers together and the imaginary numbers (terms with \( i \)) together:

$$ (2 + 8) + (3i - i) $$

Combine the real parts:

$$ 2 + 8 = 10 $$

Combine the imaginary parts:

$$ 3i - 1i = 2i $$

Combine both results to get the final complex number:

$$ 10 + 2i $$

Answer:

\( 10 + 2i \)