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Definition df-sqrt 13068
Description: Define a function whose value is the square root of a complex number. Since iff , we ensure uniqueness by restricting the range to numbers with positive real part, or numbers with 0 real part and nonnegative imaginary part. A description can be found under "Principal square root of a complex number" at http://en.wikipedia.org/wiki/Square_root. The square root symbol was introduced in 1525 by Christoff Rudolff.

See sqrtcl 13194 for its closure, sqrtval 13070 for its value, sqrtth 13197 and sqsqrti 13208 for its relationship to squares, and sqrt11i 13217 for uniqueness. (Contributed by NM, 27-Jul-1999.) (Revised by Mario Carneiro, 8-Jul-2013.)

Assertion
Ref Expression
df-sqrt
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-sqrt
StepHypRef Expression
1 csqrt 13066 . 2
2 vx . . 3
3 cc 9511 . . 3
4 vy . . . . . . . 8
54cv 1394 . . . . . . 7
6 c2 10610 . . . . . . 7
7 cexp 12166 . . . . . . 7
85, 6, 7co 6296 . . . . . 6
92cv 1394 . . . . . 6
108, 9wceq 1395 . . . . 5
11 cc0 9513 . . . . . 6
12 cre 12930 . . . . . . 7
135, 12cfv 5593 . . . . . 6
14 cle 9650 . . . . . 6
1511, 13, 14wbr 4452 . . . . 5
16 ci 9515 . . . . . . 7
17 cmul 9518 . . . . . . 7
1816, 5, 17co 6296 . . . . . 6
19 crp 11249 . . . . . 6
2018, 19wnel 2653 . . . . 5
2110, 15, 20w3a 973 . . . 4
2221, 4, 3crio 6256 . . 3
232, 3, 22cmpt 4510 . 2
241, 23wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  sqrtval  13070  sqrtf  13196
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