Complex Numbers. Flashcards
What is i ^ 4n+1 ?
i
What is i^4n+2
-1
What is i^4n+3
-i
What is i^4n+4
1
In complex numbers when is an even integer and when is n an odd integer for i^n
i=(-1)^n/2 if n is an even integer and
i=(-1)^ n-1/2 is n is an odd integer
What is z1+z2 equal to ? ; z1/z2 are complex numbers.
z1+z2=(x1+x2)+i(y1+y2)
What is z1.z2 equal to?
; z1/z2 are complex numbers.
z1.z2=(x1x2-y1y2)+i(x1y2+x2y1)
What is z1/z2 equal to ?
; z1/z2 are complex numbers.
z1/z2= = [(x1x2+y1y2)+i(x2y2-x1y2)]/x₂²+y₂²
Conjugate of a complex number z=x+iy
z(conjugate) = x -iy
Re(z) = z-z(conjugate)/2
Im(z)=z-z(conjugate)/2i
What is modulus of complex number z=x + iy
|z|= √x²+y²
What is multiplication inverse 1/z of a complex number z?
1/z= x÷x²+y² + i(-y)÷x²+y²
How is nth root of unity found out ?
z= cos 2kπ÷n + i sin 2kπ÷n k= 0,1,2.....(n-1)
On what curve does the nth root of unity lie ?
The nth root of unity lies on a unit circle and divides the circumference into n equal parts.
What is the eq of cube root of unity ?
1+ω^r+ ω^ 2r = 0 if r ain’t a multiple of 3 and 3 if r is a multiple of 3.
ω^3r=1
ω^3r+1= ω
ω^3r+2=ω²
For a complex number z, what is the centroid and incentre of triangle ABC?
Centroid :
z= (z1+z2+z3)/3
Incentre:
z= az1+bz2+cz3/a+b+c
