Applications of Harmonic Functions - Complex Analysis
Card 0 of 4
If
and
are both analytic through a domain
, which of the following is true?
If and
are both analytic through a domain
, which of the following is true?
Since
is analytic, the Cauchy-Riemann Equations give us 
Since
is analytic, the Cauchy-Riemann Equations give us
.
Putting these two results together gives us 
which implies that
is constant. Similar reasoning gives is that
is constant. This implies that
must be constant throughout
.
Since is analytic, the Cauchy-Riemann Equations give us
Since is analytic, the Cauchy-Riemann Equations give us
.
Putting these two results together gives us
which implies that is constant. Similar reasoning gives is that
is constant. This implies that
must be constant throughout
.
Compare your answer with the correct one above
If
and
are both analytic through a domain
, which of the following is true?
If and
are both analytic through a domain
, which of the following is true?
Since
is analytic, the Cauchy-Riemann Equations give us 
Since
is analytic, the Cauchy-Riemann Equations give us
.
Putting these two results together gives us 
which implies that
is constant. Similar reasoning gives is that
is constant. This implies that
must be constant throughout
.
Since is analytic, the Cauchy-Riemann Equations give us
Since is analytic, the Cauchy-Riemann Equations give us
.
Putting these two results together gives us
which implies that is constant. Similar reasoning gives is that
is constant. This implies that
must be constant throughout
.
Compare your answer with the correct one above
If
and
are both analytic through a domain
, which of the following is true?
If and
are both analytic through a domain
, which of the following is true?
Since
is analytic, the Cauchy-Riemann Equations give us 
Since
is analytic, the Cauchy-Riemann Equations give us
.
Putting these two results together gives us 
which implies that
is constant. Similar reasoning gives is that
is constant. This implies that
must be constant throughout
.
Since is analytic, the Cauchy-Riemann Equations give us
Since is analytic, the Cauchy-Riemann Equations give us
.
Putting these two results together gives us
which implies that is constant. Similar reasoning gives is that
is constant. This implies that
must be constant throughout
.
Compare your answer with the correct one above
If
and
are both analytic through a domain
, which of the following is true?
If and
are both analytic through a domain
, which of the following is true?
Since
is analytic, the Cauchy-Riemann Equations give us 
Since
is analytic, the Cauchy-Riemann Equations give us
.
Putting these two results together gives us 
which implies that
is constant. Similar reasoning gives is that
is constant. This implies that
must be constant throughout
.
Since is analytic, the Cauchy-Riemann Equations give us
Since is analytic, the Cauchy-Riemann Equations give us
.
Putting these two results together gives us
which implies that is constant. Similar reasoning gives is that
is constant. This implies that
must be constant throughout
.
Compare your answer with the correct one above