Write down the definition of the complex conjugate, bar{z} ,if z=x+iy where z,y are real numbers. Hence prove that, for any complex numbers w and z

postillan4 2021-09-11 Answered
Write down the definition of the complex conjugate, z  ,if  z=x+iy where z,y are real numbers. Hence prove that, for any complex numbers w and z,
wz=wz
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Expert Answer

berggansS
Answered 2021-09-12 Author has 91 answers

Step 1
Complex consugate
Let z be a complex number defined by z=x+iy , whre x and y are real and imaginary part.
complex consugate of z is the sum change of imaginary part.
z=xiy
let w=x1+iy1,  and  z=x2+iy2 two complex number
z=x2iy2
wz=(x1+iy1)(x2iy2)
=x1x2ix1y2+iy1x2i2y1y2
=x1x2+y1y2+i(y1x2x1y2)
Step 2
wz=(x1x2+y1y2)i(y1x2x1y2)
wz=(x1x2+y1y2)+i(x1y2y1x2)
w=x1iy1
wz=(x1iy1)(x2+iy2)
wz=(x1x2+y1y2)+i(x1y2y1x2)
Form equation 1 and equation 2
wz=wz

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