The provided mathematical expression can be transcribed as:

$\varphi_a \left( \frac{1}{16 + j16} + \frac{1}{5 - j10} + \frac{1}{20} \right) = - \frac{50 e^{j45^\circ}}{5 - j10} + \frac{20 e^{j45^\circ}}{20} - \frac{20 e^{j30^\circ}}{20}.$

Would you like me to solve this equation step by step, simplify the terms, or explain any part of it in detail? Let me know how you'd like to proceed!

5 Related Questions:

1. How do you simplify fractions with complex numbers in the denominator?
2. What is the polar representation $e^{j\theta}$ and how do you convert it to rectangular form?
3. How do you add and subtract complex numbers in the form $a + jb$?
4. Would you like a refresher on Euler’s formula and its applications in solving this equation?
5. How do we determine the magnitude and phase of complex expressions?

1 Tip:

Always convert terms to a common format (rectangular or polar) when solving equations involving complex numbers to make the calculations easier!