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# U+2102Double-Struck Capital C

U+2102 was added in Unicode version 1.1 in 1993. It belongs to the block U+2100 to U+214F Letterlike Symbols in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Uppercase Letter and is commonly used, that is, in no specific script. The character is also known as the set of complex numbers.

The glyph is a font version of the glyph Latin Capital Letter C. It has no designated width in East Asian texts. In bidirectional text it is written from left to right. When changing direction it is not mirrored. The word that U+2102 forms with similar adjacent characters prevents a line break inside it. The glyph can be confused with one other glyph.

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation ${i}^{2}=-1$; every complex number can be expressed in the form $a+bi$, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number $a+bi$, a is called the real part, and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols $C$ or C. Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world.

Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number. For example, the equation $\left(x+1{\right)}^{2}=-9$ has no real solution, because the square of a real number cannot be negative, but has the two nonreal complex solutions $-1+3i$ and $-1-3i$.

Addition, subtraction and multiplication of complex numbers can be naturally defined by using the rule ${i}^{2}=-1$ along with the associative, commutative, and distributive laws. Every nonzero complex number has a multiplicative inverse. This makes the complex numbers a field with the real numbers as a subfield.

The complex numbers also form a real vector space of dimension two, with $\left\{1,i\right\}$ as a standard basis. This standard basis makes the complex numbers a Cartesian plane, called the complex plane. This allows a geometric interpretation of the complex numbers and their operations, and conversely some geometric objects and operations can be expressed in terms of complex numbers. For example, the real numbers form the real line, which is pictured as the horizontal axis of the complex plane, while real multiples of $i$ are the vertical axis. A complex number can also be defined by its geometric polar coordinates: the radius is called the absolute value of the complex number, while the angle from the positive real axis is called the argument of the complex number. The complex numbers of absolute value one form the unit circle. Adding a fixed complex number to all complex numbers defines a translation in the complex plane, and multiplying by a fixed complex number is a similarity centered at the origin (dilating by the absolute value, and rotating by the argument). The operation of complex conjugation is the reflection symmetry with respect to the real axis.

The complex numbers form a rich structure that is simultaneously an algebraically closed field, a commutative algebra over the reals, and a Euclidean vector space of dimension two.

## Representations

System Representation
8450
UTF-8 E2 84 82
UTF-16 21 02
UTF-32 00 00 21 02
URL-Quoted %E2%84%82
HTML hex reference &#x2102;
Wrong windows-1252 Mojibake â„‚
HTML named entity &Copf;
HTML named entity &complexes;
alias the set of complex numbers
LATEX \mathbb{C}

## Complete Record

Property Value
Age (age) 1.1 (1993)
Unicode Name (na) DOUBLE-STRUCK CAPITAL C
Unicode 1 Name (na1) DOUBLE-STRUCK C
Block (blk) Letterlike Symbols
General Category (gc) Uppercase Letter
Script (sc) Common
Bidirectional Category (bc) Left To Right
Combining Class (ccc) Not Reordered
Decomposition Type (dt) font
Decomposition Mapping (dm) Latin Capital Letter C
Lowercase (Lower)
Simple Lowercase Mapping (slc) Double-Struck Capital C
Lowercase Mapping (lc) Double-Struck Capital C
Uppercase (Upper)
Simple Uppercase Mapping (suc) Double-Struck Capital C
Uppercase Mapping (uc) Double-Struck Capital C
Simple Titlecase Mapping (stc) Double-Struck Capital C
Titlecase Mapping (tc) Double-Struck Capital C
Case Folding (cf) Double-Struck Capital C
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Composition Exclusion (CE)
Case Ignorable (CI)
Changes When Casefolded (CWCF)
Changes When Casemapped (CWCM)
Changes When NFKC Casefolded (CWKCF)
Changes When Lowercased (CWL)
Changes When Titlecased (CWT)
Changes When Uppercased (CWU)
Cased (Cased)
Full Composition Exclusion (Comp_Ex)
Default Ignorable Code Point (DI)
Dash (Dash)
Deprecated (Dep)
Diacritic (Dia)
Emoji Modifier Base (EBase)
Emoji Component (EComp)
Emoji Modifier (EMod)
Emoji Presentation (EPres)
Emoji (Emoji)
Extender (Ext)
Extended Pictographic (ExtPict)
FC NFKC Closure (FC_NFKC) Latin Small Letter C
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hyphen (Hyphen)
ID Continue (IDC)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
IDSU (IDSU) 0
ID_Compat_Math_Continue (ID_Compat_Math_Continue) 0
ID_Compat_Math_Start (ID_Compat_Math_Start) 0
Ideographic (Ideo)
InCB (InCB) None
Indic Mantra Category (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
Jamo Short Name (JSN)
Join Control (Join_C)
Logical Order Exception (LOE)
Math (Math)
Noncharacter Code Point (NChar)
NFC Quick Check (NFC_QC) Yes
NFD Quick Check (NFD_QC) Yes
NFKC Casefold (NFKC_CF) Latin Small Letter C
NFKC Quick Check (NFKC_QC) No
NFKC_SCF (NFKC_SCF) Latin Small Letter C
NFKD Quick Check (NFKD_QC) No
Other Alphabetic (OAlpha)
Other Default Ignorable Code Point (ODI)
Other Grapheme Extend (OGr_Ext)
Other ID Continue (OIDC)
Other ID Start (OIDS)
Other Lowercase (OLower)
Other Math (OMath)
Other Uppercase (OUpper)
Prepended Concatenation Mark (PCM)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Regional Indicator (RI)
Sentence Break (SB) Upper
Soft Dotted (SD)
Sentence Terminal (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) Alphabetic Letter
White Space (WSpace)
XID Continue (XIDC)
XID Start (XIDS)
Expands On NFC (XO_NFC)
Expands On NFD (XO_NFD)
Expands On NFKC (XO_NFKC)
Expands On NFKD (XO_NFKD)
Bidi Paired Bracket (bpb) Double-Struck Capital C
Bidi Paired Bracket Type (bpt) None
East Asian Width (ea) neutral
Hangul Syllable Type (hst) Not Applicable
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Joining Type (jt) Non Joining
Line Break (lb) Alphabetic
Numeric Type (nt) none
Numeric Value (nv) not a number
Simple Case Folding (scf) Double-Struck Capital C
Script Extension (scx)
Vertical Orientation (vo) R