Question
Which expression simplifies to a complex number in the form \( \mathrm{a}+\mathrm{bi} \) where b is not equal to 0 ? \( \begin{array}{l}\text { A. } 3(3-4 i) \\ \text { B. }(3 i)(4 i) \\ \text { C. }(3-4 i)+(3+4 i) \\ \text { D. }(4+3 i)-(5+3 i)\end{array} \)
Ask by Todd Vaughn. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Option A simplifies to \( 9 - 12i \), which is a complex number with \( b \neq 0 \).
Solution
To determine which expression simplifies to a complex number in the form \( \mathrm{a} + \mathrm{bi} \) where \( b \neq 0 \), let's evaluate each option:
**A. \( 3(3 - 4i) \)**
\[
3(3 - 4i) = 9 - 12i
\]
This is in the form \( 9 + (-12)i \), where \( b = -12 \neq 0 \).
**B. \( (3i)(4i) \)**
\[
(3i)(4i) = 12i^2 = 12(-1) = -12
\]
This simplifies to \( -12 \), which is a real number (\( b = 0 \)).
**C. \( (3 - 4i) + (3 + 4i) \)**
\[
(3 - 4i) + (3 + 4i) = 6 + 0i
\]
This simplifies to \( 6 \), which is a real number (\( b = 0 \)).
**D. \( (4 + 3i) - (5 + 3i) \)**
\[
(4 + 3i) - (5 + 3i) = -1 + 0i
\]
This simplifies to \( -1 \), which is a real number (\( b = 0 \)).
Among the options, only **Option A** results in a complex number where the imaginary part \( b \) is not zero.
**Answer:** A
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
Let's simplify each expression and see which one yields a complex number in the form \( a + bi \) where \( b \neq 0 \). A: \( 3(3-4i) = 9 - 12i \) (This gives \( b = -12 \), so this option qualifies.) B: \( (3i)(4i) = 12(i^2) = 12(-1) = -12 \) (This is a real number, \( b = 0 \).) C: \( (3-4i) + (3+4i) = 3 - 4i + 3 + 4i = 6 + 0i \) (This is also a real number, \( b = 0 \).) D: \( (4+3i) - (5+3i) = 4 + 3i - 5 - 3i = -1 + 0i \) (This is again a real number, \( b = 0 \).) The only expression that simplifies to \( a + bi \) with \( b \neq 0 \) is: **Answer: A.**
