Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Select all the correct answers.

Which expressions are equivalent to the given complex number [tex]45 + 2i[/tex]?

A. [tex](9 + 4i) + 2(4 + 7i)(1 - 2i)[/tex]
B. [tex](13 + 4i) + (32 - 6i)[/tex]
C. [tex](2 + 8i) + 2(9 + 6i)(1 - i)[/tex]
D. [tex](9 + 4i) + (36 - 2i)[/tex]
E. [tex](13 + 4i) + 2(7 + 2i)(2 - i)[/tex]
F. [tex](2 + 8i) + (30 - 6i)[/tex]

Sagot :

GinnyAnswer
To determine which of the given expressions are equivalent to the complex number [tex]$45 + 2i$[/tex], we need to evaluate each expression step-by-step and compare the results.

1. Expression 1:
[tex]\[ (9 + 4i) + 2(4 + 7i)(1 - 2i) \][/tex]
Evaluating this, we find:
[tex]\[ (45 + 2i) \][/tex]
This is equivalent to the given complex number [tex]$45 + 2i$[/tex].

2. Expression 2:
[tex]\[ (13 + 4i) + (32 - 6i) \][/tex]
Evaluating this, we find:
[tex]\[ (45 - 2i) \][/tex]
This is not equivalent to the given complex number [tex]$45 + 2i$[/tex].

3. Expression 3:
[tex]\[ (2 + 8i) + 2(9 + 6i)(1 - i) \][/tex]
Evaluating this, we find:
[tex]\[ (32 + 2i) \][/tex]
This is not equivalent to the given complex number [tex]$45 + 2i$[/tex].

4. Expression 4:
[tex]\[ (9 + 4i) + (36 - 2i) \][/tex]
Evaluating this, we find:
[tex]\[ (45 + 2i) \][/tex]
This is equivalent to the given complex number [tex]$45 + 2i$[/tex].

5. Expression 5:
[tex]\[ (13 + 4i) + 2(7 + 2i)(2 - i) \][/tex]
Evaluating this, we find:
[tex]\[ (45 - 2i) \][/tex]
This is not equivalent to the given complex number [tex]$45 + 2i$[/tex].

6. Expression 6:
[tex]\[ (2 + 8i) + (30 - 6i) \][/tex]
Evaluating this, we find:
[tex]\[ (32 + 2i) \][/tex]
This is not equivalent to the given complex number [tex]$45 + 2i$[/tex].

Thus, the expressions that are equivalent to [tex]$45 + 2i$[/tex] are:
[tex]\[ (9 + 4i) + 2(4 + 7i)(1 - 2i) \][/tex]
and
[tex]\[ (9 + 4i) + (36 - 2i) \][/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.