Complex Numbers
Complex Numbers
Allen Star Batch
Grade 11
Question:
Complex numbers $z_1, z_2, z_3$ and $z_4$ correspond to the points $A, B, C$ and $D$, respectively, on a circle $|z| = 1$. If $z_1 + z_2 + z_3 + z_4 = 0$, then $ABCD$ is necessarily
a triangle
a square
a rhombus
a parallelogram
Step-by-Step Solution
Key Concept: The difference between total selections and selections excluding one element equals selections of one fewer element.
The number of visits a teacher makes equals the number of ways to select 5 students from 25, which is $^{25}C_5$. For a particular student, the number of trips is the number of ways to select 4 remaining students from 24, which is $^{24}C_4$. The difference is $^{25}C_5 - ^{24}C_4 = ^{24}C_5$.
Correct Answer: 1,4