### Complex Numbers: Exercise on a + bi Form#### InstructionsWrite the complex numbers in Problems 13–32 in the form \( a + bi \) where \( a \) and \( b \) are real numbers.---#### Problems1. \((2 - 6i) + (23 - 14i)\)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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Answered: Write the complex numbers in Problems…

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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Topic under advanced math, addition,subtraction,multiplication and division of complex numbers