Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Which complex number is equivalent to this expression?

[tex]\[7 + (9 + 27i) - 2(25 - 11i)\][/tex]

A. [tex]\[66 - 49i\][/tex]

B. [tex]\[-34 + 5i\][/tex]

C. [tex]\[68 + 5i\][/tex]

D. [tex]\[-34 + 49i\][/tex]

Sagot :

GinnyAnswer
To solve the given complex number expression step by step, let's break it down and simplify it systematically.

Given expression:
[tex]\[ 7 + (9 + 27i) - 2(25 - 11i) \][/tex]

First, apply the distributive property to [tex]\( -2(25 - 11i) \)[/tex]:
[tex]\[ -2 \times 25 = -50 \][/tex]
[tex]\[ -2 \times (-11i) = 22i \][/tex]
So, the expression [tex]\( -2(25 - 11i) \)[/tex] simplifies to:
[tex]\[ -50 + 22i \][/tex]

Now rewrite the entire expression with this simplified form:
[tex]\[ 7 + (9 + 27i) - 50 + 22i \][/tex]

Combine the real parts and the imaginary parts separately:
1. Real parts: [tex]\( 7 + 9 - 50 \)[/tex]
[tex]\[ 7 + 9 = 16 \][/tex]
[tex]\[ 16 - 50 = -34 \][/tex]

2. Imaginary parts: [tex]\( 27i + 22i \)[/tex]
[tex]\[ 27i + 22i = 49i \][/tex]

Thus, the combined simplified form is:
[tex]\[ -34 + 49i \][/tex]

Hence, the equivalent complex number is:
[tex]\[ \boxed{-34 + 49i} \][/tex]

So, the correct answer is:
D. [tex]\(-34 + 49i\)[/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.