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.
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.
Complex
.
BigOperators
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Imports
Init
Mathlib.Algebra.BigOperators.Expect
Mathlib.Data.Complex.Basic
Imported by
Complex
.
ofReal_prod
Complex
.
ofReal_sum
Complex
.
ofReal_expect
Complex
.
re_sum
Complex
.
re_expect
Complex
.
im_sum
Complex
.
im_expect
Finite sums and products of complex numbers
#
source
@[simp]
theorem
Complex
.
ofReal_prod
{α :
Type
u_1}
(s :
Finset
α
)
(f :
α
→
ℝ
)
:
↑
(∏
i
∈
s
,
f
i
)
=
∏
i
∈
s
,
↑
(
f
i
)
source
@[simp]
theorem
Complex
.
ofReal_sum
{α :
Type
u_1}
(s :
Finset
α
)
(f :
α
→
ℝ
)
:
↑
(∑
i
∈
s
,
f
i
)
=
∑
i
∈
s
,
↑
(
f
i
)
source
@[simp]
theorem
Complex
.
ofReal_expect
{α :
Type
u_1}
(s :
Finset
α
)
(f :
α
→
ℝ
)
:
↑
(
s
.expect
fun (
i
:
α
) =>
f
i
)
=
s
.expect
fun (
i
:
α
) =>
↑
(
f
i
)
source
@[simp]
theorem
Complex
.
re_sum
{α :
Type
u_1}
(s :
Finset
α
)
(f :
α
→
ℂ
)
:
(∑
i
∈
s
,
f
i
)
.re
=
∑
i
∈
s
,
(
f
i
)
.re
source
@[simp]
theorem
Complex
.
re_expect
{α :
Type
u_1}
(s :
Finset
α
)
(f :
α
→
ℂ
)
:
(
s
.expect
fun (
i
:
α
) =>
f
i
)
.re
=
s
.expect
fun (
i
:
α
) =>
(
f
i
)
.re
source
@[simp]
theorem
Complex
.
im_sum
{α :
Type
u_1}
(s :
Finset
α
)
(f :
α
→
ℂ
)
:
(∑
i
∈
s
,
f
i
)
.im
=
∑
i
∈
s
,
(
f
i
)
.im
source
@[simp]
theorem
Complex
.
im_expect
{α :
Type
u_1}
(s :
Finset
α
)
(f :
α
→
ℂ
)
:
(
s
.expect
fun (
i
:
α
) =>
f
i
)
.im
=
s
.expect
fun (
i
:
α
) =>
(
f
i
)
.im