Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
ANSWER
[tex]\begin{gathered} z\text{ = -}\frac{17}{20}\text{ + }\frac{19}{20}i \\ \text{option D} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
Given information
[tex]z\text{ = }\frac{4\text{ + 7i}}{2\text{ - 6i}}[/tex]Step 1: We need to find the conjugate of the denominator
[tex]\begin{gathered} \text{The conjugate of 2 - 6i is 2 + 6i} \\ \text{Conjugate = 2 + 6i} \end{gathered}[/tex]Step 2: Multiply the conjugate by the numerator and the denominator
[tex]\frac{4\text{ + 7i}}{2\text{ - 6i}}\times\text{ }\frac{2\text{ +6i}}{2\text{ + 6i}}[/tex]Step 3: Simplify the above expression
[tex]\begin{gathered} z=\frac{(4\times2)\text{ + (4}\times6i)\text{ + (7i }\times2)\text{ + (7i}\times6i)}{(2\times2)\text{ + (2}\times6i)-(6i\times2)-(6i\times6i)} \\ \text{ Expand the parentheses} \\ z=\frac{8+24i+14i+42i^2}{4+12i-12i-36i^2} \\ \text{Recall, }i^2\text{ = -1} \\ \text{Substitute i}^2\text{ = -1 into the expression} \\ z=\frac{8\text{ + 38i + 42(-1)}}{4\text{ - }36(-1)} \\ \\ z=\frac{8\text{ + 38i - 42}}{4\text{ + 36}} \\ \\ z=\frac{8\text{ - 42 + 38i}}{40} \\ z=\frac{-34\text{ + 38i}}{40} \\ z=\text{ }\frac{-34}{40}\text{ + }\frac{38i}{40} \\ z\text{ = -}\frac{17}{20}\text{ + }\frac{19}{20}i \end{gathered}[/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.