IIT JEE , AIEEE Forum - Mathematics , Algebra

rtiit

What is De Moivre's theorem??

anchal_1991

(cos

+sin

)ⁿ=cos n

+sin n

rathin_123

de moivre's thyorem is

if [cos@+isin@]^n then =cosn@+insin@

racerix

Here is De Moivre's Theorem:

1) If z1 = cos(a1) + isin(a1)
    z2 = cos(a2) + isin(a2)

then z1.z2 = [cos(a1) + isin(a1)][cos(a2) + isin(a2)]
                       = cos(a1+a2)+isin(a1+a2)

similarly z1.z2.z3..... = [cos(a1+a2+a3....) + isin(a1+a2+a3....)]

2) Also,
     [cos(a) + isin(a)]ⁿ = cos(na) + isin(na)
     [cos(a) + isin(a)]^-n = cos(na) - isin(na)
     [cos(a) - isin(a)]ⁿ = cos(na) - isin(na)

rtiit

thn what did anchal say??

rtiit

is that valid too???

anchal_1991

its d basic one it only comes wen we talk of demoivres theorem
nw frm dis u can derive dat

1._{[0 ]}

^{[n-1 ]} cos (2k

/n)=1
similarly for sin its 0

racerix

Yup,

Here

[I used a1 and a2] is used in polar form of complex number (angle of position 'z' in argand plane) known as amplitude

Amplitude of z,

is given by tan

= y/x , it depends on quadrant where point (x,y) exist is argand plane

So that

= tan^-1y/x

Ask & Discuss Questions with Community & Experts