So I’m thinking C because they both have a lot to do with design here is my evidence. Structural engineering is a component of civil engineering which focuses on the design and development of infrastructures such as bridges, skyscrapers, dams. Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment. I may be wrong but hope this helped!
Answer:
- |z*| = r , ∠(z*) = -∅
- |z²| = r² , ∠(z²) = 2∅
- |jz| = r , ∠(jz) = ∅
- |zz*| = r² , ∠(zz*) = 0
- |z/z*| = 1 , ∠(z/z*) = 2∅
- |1/z| = r ⁻¹ , ∠(1/z) = -∅
Explanation:
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1.) The * mean you take the conjugate of the value. This means you change the sign of the imaginary part, so if it's positive, turn it negative and vice versa.
2.) The magnitude with an exponent can have the exponent moved outside the magnitude. |zⁿ| = |z|ⁿ
The angle multiplies with its exponent instead. ∠zⁿ = n∠z
3.) This part is just testing if you can convert the number using the eulers formula and convert back.
The magnitude could be found using the distance formula. √(R² + I²)
The angle could be found using tan⁻¹(Imaginary/Real).
4.) Magnitude of a product could be split up. |zv| = |z|·|v|
Angle of a product could be splitted up and added. ∠(zv) = ∠z + ∠v
5.) Simplify it first using some algebra and use the euler's identity to identify the magnitude and angle. It takes in a form like this:
![z=Ae^{j\theta}](https://tex.z-dn.net/?f=z%3DAe%5E%7Bj%5Ctheta%7D)
A is your magnitude, ∅ is your angle.
6.) Same rule as part 2
False, there are negative side affects that have just as much if not more impact. One example of this is the effect on natural habit.
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