Question
Need help for calcul:
( 1/2 ( -1 + i√3 )) ^2
thanks for your help
( 1/2 ( -1 + i√3 )) ^2
thanks for your help
Answers
drwls
That can be rewritten
(1/2)^2 * (-1 + i√3)^2
= (1/4)[1 -2i√3 -3]
= (-1/2)[1 +i√3]
(1/2)^2 * (-1 + i√3)^2
= (1/4)[1 -2i√3 -3]
= (-1/2)[1 +i√3]
drwls
Note that you are squaring a complex number that has a magnitude (modulus) of 1.
The number that is being squared can be written
e^(i*2*pi/3) = cos(2*pi/3) + i sin(2*pi/3)
The square of that number is e^(i*4*pi/3)
which agrees with the previous result.
The number that is being squared can be written
e^(i*2*pi/3) = cos(2*pi/3) + i sin(2*pi/3)
The square of that number is e^(i*4*pi/3)
which agrees with the previous result.