maharjanprasana11
maharjanprasana11 maharjanprasana11
  • 04-01-2022
  • Mathematics
contestada

Using De-Moivre's theorem, prove that i^2= -1.​

Respuesta :

LammettHash
LammettHash LammettHash
  • 04-01-2022

Write i in trigonometric form. Since |i| = 1 and arg(i) = π/2, we have

i = exp(i π/2) = cos(π/2) + i sin(π/2)

By DeMoivre's theorem,

i² = exp(i π/2)² = exp(i π) = cos(π) + i sin(π)

and it follows that i² = -1 since cos(π) = -1 and sin(π) = 0.

Answer Link

Otras preguntas

What is 700,000,000,000 written in scientific notation?
​If cultural pluralism were part of a U.S. school, how would that affect a group of immigrant students from Portugal?
what acceleration does the force of earth's gravity produce It varies depending on how long it has been falling. It changes direction every 9.8 meters 9.8 m/s/s
the people elect representatives to make laws and conduct government
Mario borrows $4800 for 8.5 years at a fixed rate of simple interest. At the end of that time, he owes $8000. What interest rate is he being charged?
The least common multiple of 3,9,15
The Protestant leader who made the first major translation of the Bible into English was: Martin Luther John Wycliffe John Huss John Calvin
What are the 3 bacterial shapes and what is their scientific name
Would a field with a wid
Many believe the United States Constitution was made to be inefficient, meaning it does not create a system that works quickly. If this is true, why would the F