Applications of Harmonic Functions - Complex Analysis
Card 1 of 4
If 
and 
are both analytic through a domain 
, which of the following is true?
If
Tap to reveal answer
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
Since
Putting these two results together gives us
which implies that
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If and are both analytic through a domain , which of the following is true?
If
Tap to reveal answer
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
Since
Putting these two results together gives us
which implies that
← Didn't Know|Knew It →
If and are both analytic through a domain , which of the following is true?
If
Tap to reveal answer
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
Since
Putting these two results together gives us
which implies that
← Didn't Know|Knew It →
If and are both analytic through a domain , which of the following is true?
If
Tap to reveal answer
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
Since
Putting these two results together gives us
which implies that
← Didn't Know|Knew It →