Subtract (3 + 2i) from (–9 – 8i). –17 – 5i –6 – 6i –12 – 10i 12 + 10
The correct answer and explanation is:
Correct Answer: –12 – 10i
Step-by-step Calculation:
We are asked to subtract the complex number (3 + 2i) from (–9 – 8i).
In math terms, this means: (–9–8i)–(3+2i)(–9 – 8i) – (3 + 2i)
To subtract complex numbers, subtract the real parts and then the imaginary parts separately.
1. Subtract the real parts:
–9–3=–12–9 – 3 = –12
2. Subtract the imaginary parts:
–8i–2i=–10i–8i – 2i = –10i
Final Answer:
–12–10i\boxed{–12 – 10i}
300-Word Explanation:
Complex numbers are composed of two parts: a real part and an imaginary part. The imaginary unit “i” is defined as the square root of –1. A complex number looks like this:
a + bi, where a is the real part and b is the coefficient of the imaginary part.
In this problem, we are subtracting two complex numbers:
(–9 – 8i) and (3 + 2i).
The expression “subtract (3 + 2i) from (–9 – 8i)” means we take the second number and subtract the first: (–9–8i)–(3+2i)(–9 – 8i) – (3 + 2i)
To solve this, we treat the real and imaginary parts separately.
Start with the real parts:
- The real part of (–9 – 8i) is –9.
- The real part of (3 + 2i) is 3.
- So, –9 – 3 = –12.
Next, handle the imaginary parts:
- The imaginary part of (–9 – 8i) is –8i.
- The imaginary part of (3 + 2i) is 2i.
- So, –8i – 2i = –10i.
When we combine the results, we get: –12–10i–12 – 10i
This is our final simplified answer. Subtracting complex numbers this way is similar to subtracting binomials: handle each part (real and imaginary) separately. This keeps your work clear and accurate.
✅ Answer: –12 – 10i.