Show that if z_{1} and are complex numbers then \bar{\frac{z_{1}}{z_{2}}}=\frac{\bar{z_{1}}}{\bar{z_{2}}}

Ellie Castro

Ellie Castro

Answered question

2022-04-23

Show that if z1 and are complex numbers then
z1z2=z1z2

Answer & Explanation

Makayla Santiago

Makayla Santiago

Beginner2022-04-24Added 19 answers

Step 1
Given z1 and z2 are two complex numbers and we have to show,
(z1z2)=z1z2 and z20
Step 2
Since we know that,
z1z2=z1z2
(z1z2)=z1(1z2)=z1z2
Now, we have to prove this (1z2)=1z2
Let z2=x2+iy2
(1x2+iy2)=((x2iy2)(x2+iy2)(x2iy2))=((x2iy2)(x22+y22))
=((x2iy2)(x22+y22))x22+y22 is a real number. 1x22+y22=1x22+y22
=(x2+iy2)(x22+y22)
and 1z2=1x2+iy2=1x2iy2=(x2+iy2)(x22+y22)
Hence (1z2)=1z2
(1z2)=1z2
(z1z2)=z1z2
Hence Proved.

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