What is (1+i)^{4}+(1-i)^{4} equal to, where i=\sqrt{-1}?
- A. 4
- B. 0
- C. -4
- D. -8 ✓
Correct Answer: D. -8
Explanation
First, square the inner terms: (1+i)^2 = 1 + i^2 + 2i = 2i and (1-i)^2 = 1 + i^2 - 2i = -2i. Now, raise these to the power of 2: (2i)^2 + (-2i)^2 = 4i^2 + 4i^2 = -4 - 4 = -8.
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?