Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Ask your questions and receive precise answers from experienced professionals across different disciplines. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To determine the sum of the complex numbers [tex]\( z_1 \)[/tex] and [tex]\( z_2 \)[/tex], follow these steps:
Given:
[tex]\[ z_1 = 2 + \sqrt{3} i \][/tex]
[tex]\[ z_2 = 1 - \sqrt{3} i \][/tex]
Step 1: Write down the formula for the sum of two complex numbers.
[tex]\[ z_{\text{sum}} = z_1 + z_2 \][/tex]
Step 2: Substitute the given values into the sum formula.
[tex]\[ z_{\text{sum}} = (2 + \sqrt{3} i) + (1 - \sqrt{3} i) \][/tex]
Step 3: Combine the real parts of [tex]\( z_1 \)[/tex] and [tex]\( z_2 \)[/tex]:
[tex]\[ \text{Real part of } z_{\text{sum}} = 2 + 1 = 3 \][/tex]
Step 4: Combine the imaginary parts of [tex]\( z_1 \)[/tex] and [tex]\( z_2 \)[/tex]:
[tex]\[ \text{Imaginary part of } z_{\text{sum}} = (\sqrt{3}) i - (\sqrt{3}) i = 0 i \][/tex]
Step 5: Combine the real and imaginary parts to write the final result:
[tex]\[ z_{\text{sum}} = 3 + 0 i = 3 \][/tex]
Thus, the sum of [tex]\( z_1 \)[/tex] and [tex]\( z_2 \)[/tex] is [tex]\( 3 \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{3} \][/tex]
Given:
[tex]\[ z_1 = 2 + \sqrt{3} i \][/tex]
[tex]\[ z_2 = 1 - \sqrt{3} i \][/tex]
Step 1: Write down the formula for the sum of two complex numbers.
[tex]\[ z_{\text{sum}} = z_1 + z_2 \][/tex]
Step 2: Substitute the given values into the sum formula.
[tex]\[ z_{\text{sum}} = (2 + \sqrt{3} i) + (1 - \sqrt{3} i) \][/tex]
Step 3: Combine the real parts of [tex]\( z_1 \)[/tex] and [tex]\( z_2 \)[/tex]:
[tex]\[ \text{Real part of } z_{\text{sum}} = 2 + 1 = 3 \][/tex]
Step 4: Combine the imaginary parts of [tex]\( z_1 \)[/tex] and [tex]\( z_2 \)[/tex]:
[tex]\[ \text{Imaginary part of } z_{\text{sum}} = (\sqrt{3}) i - (\sqrt{3}) i = 0 i \][/tex]
Step 5: Combine the real and imaginary parts to write the final result:
[tex]\[ z_{\text{sum}} = 3 + 0 i = 3 \][/tex]
Thus, the sum of [tex]\( z_1 \)[/tex] and [tex]\( z_2 \)[/tex] is [tex]\( 3 \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{3} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.