If z \neq 0 is a complex number, then what is \text{amp}(z)+\text{amp}(\overline{z}) equal to?
- A. 0 ✓
- B. \pi/2
- C. \pi
- D. 2\pi
Correct Answer: A. 0
Explanation
Let z = r e^{i\theta}. Then its conjugate is \overline{z} = r e^{-i\theta}. The amplitude of z is \theta and the amplitude of \overline{z} is -\theta. Their sum is \theta + (-\theta) = 0.
Related questions on Algebra
- How many four-digit natural numbers are there such that <strong>ALL</strong> of the digits are odd?
- What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
- If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a...
- Consider the following statements : 1. If f is the subset of Z\times Z defined by f=\{(xy,x-y);x,y\in Z\}, then f is a function from...
- For how many quadratic equations, the sum of roots is equal to the product of roots?