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Write the complex numbers in Problems 13-32 in the form a + bi where a and b are real numbers. 13. (2- 6i) + (23 – 14i) JA. (7+ i)(2 – 5i) 5 15. 4+3i बर्षश 16. V-12

Write the complex numbers in Problems 13-32 in the form a + bi where a and b are real numbers. 13. (2- 6i) + (23 – 14i) JA. (7+ i)(2 – 5i) 5 15. 4+3i बर्षश 16. V-12

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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### Complex Numbers: Exercise on a + bi Form #### Instructions Write the complex numbers in Problems 13–32 in the form \( a + bi \) where \( a \) and \( b \) are real numbers. --- #### Problems 1. \((2 - 6i) + (23 - 14i)\) 2. \((7 + i)(2 - 5i)\) 3. \(\frac{5}{4 + 3i}\) 4. \(\sqrt{-12}\) 5. \(\sqrt{-81} - \sqrt{-4}\) 6. \(3\sqrt{-25} - 4\sqrt{-64}\) 7. \(2\sqrt{-16} - 5\sqrt{-1}\) 8. \((7 + 5i) - (12 - 11i)\) 9. \((5 + 2i)^2\) 10. \(6(3 + 4i) - 2i(i + 5)\) 11. \(\frac{1 + 4i}{6 + 3i}\) 12. \((2 - 8i)(2 + 8i)\) 13. \(\frac{1}{4 - 5i}\) 14. \((3 + 8i) + 2(4 - 7i)\) 15. \((9 - 7i) - 3(5 + i)\) #### Notes on Selected Problems - **Problem 13**: Expression: \((2 - 6i) + (23 - 14i)\) - **Solution**: Combine real and imaginary parts separately. - Real part: \(2 + 23 = 25\) - Imaginary part: \(-6i - 14i = -20i\) - **Result in \( a + bi \) form**: \(25 - 20i\) - **Problem 14**: Expression: \((7 + i)(2 - 5i)\) - **Solution**: Expand using distributive property and combine like terms. - First, distribute \( (7 + i) \): \(7 \cdot 2 + 7 \cdot (-5i) + i \cdot 2 + i \cdot (-5i)\) - Combine and simplify
Transcribed Image Text:### Complex Numbers: Exercise on a + bi Form #### Instructions Write the complex numbers in Problems 13–32 in the form \( a + bi \) where \( a \) and \( b \) are real numbers. --- #### Problems 1. \((2 - 6i) + (23 - 14i)\) 2. \((7 + i)(2 - 5i)\) 3. \(\frac{5}{4 + 3i}\) 4. \(\sqrt{-12}\) 5. \(\sqrt{-81} - \sqrt{-4}\) 6. \(3\sqrt{-25} - 4\sqrt{-64}\) 7. \(2\sqrt{-16} - 5\sqrt{-1}\) 8. \((7 + 5i) - (12 - 11i)\) 9. \((5 + 2i)^2\) 10. \(6(3 + 4i) - 2i(i + 5)\) 11. \(\frac{1 + 4i}{6 + 3i}\) 12. \((2 - 8i)(2 + 8i)\) 13. \(\frac{1}{4 - 5i}\) 14. \((3 + 8i) + 2(4 - 7i)\) 15. \((9 - 7i) - 3(5 + i)\) #### Notes on Selected Problems - **Problem 13**: Expression: \((2 - 6i) + (23 - 14i)\) - **Solution**: Combine real and imaginary parts separately. - Real part: \(2 + 23 = 25\) - Imaginary part: \(-6i - 14i = -20i\) - **Result in \( a + bi \) form**: \(25 - 20i\) - **Problem 14**: Expression: \((7 + i)(2 - 5i)\) - **Solution**: Expand using distributive property and combine like terms. - First, distribute \( (7 + i) \): \(7 \cdot 2 + 7 \cdot (-5i) + i \cdot 2 + i \cdot (-5i)\) - Combine and simplify
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