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

How does the 8th amendment protect citizens?
What made it possible for at least some european christians of the renaissance era to embrace both the pagan aristotle and the islamic ibn rushd?
lucie can walk about 3 4/5 miles each hour. about how far can she walk in 2 hours 45 minutes?
PLEASE HELP <3 Which historical value do the following lines discuss? MERCUTIO: You gave us the counterfeit fairly last night. ROMEO: Good morrow to you
After passing another car, you should not pull back in front of it until you _____________.
Names of any satellites or robots that have explored neptune close-up
HELP ME (: 15 pts! I’m stuck
Can anyone help me with #7?
The ships icons on the war of 1812 map represent what aspect of the war? A: British naval blockade. B: American naval blockade. C:American whaling fleet. Or D:
A polynomial function with real coefficients has real zeros true or false