diff --git a/crates/els/semantic.rs b/crates/els/semantic.rs
index 4a48d648c..58bb5920e 100644
--- a/crates/els/semantic.rs
+++ b/crates/els/semantic.rs
@@ -141,9 +141,11 @@ impl ASTSemanticState {
             Expr::Literal(lit) => {
                 let typ = match lit.token.kind {
                     TokenKind::StrLit => SemanticTokenType::STRING,
-                    TokenKind::NatLit | TokenKind::IntLit | TokenKind::RatioLit => {
-                        SemanticTokenType::NUMBER
-                    }
+                    TokenKind::NatLit
+                    | TokenKind::IntLit
+                    | TokenKind::RatioLit
+                    | TokenKind::ImLit
+                    | TokenKind::ComplexLit => SemanticTokenType::NUMBER,
                     _ => SemanticTokenType::VARIABLE,
                 };
                 let token = self.gen_token(lit.loc(), typ);
diff --git a/crates/erg_compiler/codegen.rs b/crates/erg_compiler/codegen.rs
index 9085c9dfd..2607aa7ac 100644
--- a/crates/erg_compiler/codegen.rs
+++ b/crates/erg_compiler/codegen.rs
@@ -3145,6 +3145,14 @@ impl PyCodeGenerator {
                     self.emit_push_null();
                     self.emit_load_name_instr(Identifier::public("Ratio"));
                 }
+                Imag => {
+                    self.emit_push_null();
+                    self.emit_load_name_instr(Identifier::public("Imag"));
+                }
+                Complex => {
+                    self.emit_push_null();
+                    self.emit_load_name_instr(Identifier::public("Complex"));
+                }
                 Float => {
                     self.emit_push_null();
                     self.emit_load_name_instr(Identifier::public("Float"));
diff --git a/crates/erg_compiler/context/compare.rs b/crates/erg_compiler/context/compare.rs
index 1e2bf249f..649dea0a4 100644
--- a/crates/erg_compiler/context/compare.rs
+++ b/crates/erg_compiler/context/compare.rs
@@ -1661,7 +1661,7 @@ impl Context {
     // sup/inf({±∞}) = ±∞ではあるが、Inf/NegInfにはOrdを実装しない
     fn sup(&self, t: &Type) -> Option<TyParam> {
         match t {
-            Int | Nat | Ratio | Float => Some(TyParam::value(Inf)),
+            Int | Nat | Ratio | Imag | Complex | Float => Some(TyParam::value(Inf)),
             Refinement(refine) => {
                 let mut maybe_max = None;
                 for pred in refine.pred.ands() {
@@ -1688,7 +1688,7 @@ impl Context {
 
     fn inf(&self, t: &Type) -> Option<TyParam> {
         match t {
-            Int | Ratio | Float => Some(TyParam::value(-Inf)),
+            Int | Ratio | Imag | Complex | Float => Some(TyParam::value(-Inf)),
             Nat => Some(TyParam::value(0usize)),
             Refinement(refine) => {
                 let mut maybe_min = None;
diff --git a/crates/erg_compiler/context/eval.rs b/crates/erg_compiler/context/eval.rs
index 6d38c4dc3..4538fd20e 100644
--- a/crates/erg_compiler/context/eval.rs
+++ b/crates/erg_compiler/context/eval.rs
@@ -10,6 +10,7 @@ use erg_common::ratio::Ratio;
 use erg_common::set::Set;
 use erg_common::shared::Shared;
 use erg_common::traits::{Locational, Stream};
+use erg_common::{complex::Complex, imag::Imag};
 use erg_common::{dict, fmt_vec, fn_name, option_enum_unwrap, set, Triple};
 use erg_common::{ArcArray, Str};
 use OpKind::*;
@@ -1394,7 +1395,9 @@ impl Context {
             ValueObj::Bool(b) => Ok(ValueObj::Nat(b as u64 + 1)),
             ValueObj::Nat(n) => Ok(ValueObj::Nat(n + 1)),
             ValueObj::Int(n) => Ok(ValueObj::Int(n + 1)),
-            ValueObj::Ratio(r) => Ok(ValueObj::Ratio(r + Ratio::new(1, 1))),
+            ValueObj::Ratio(r) => Ok(ValueObj::Ratio(r + Ratio::int_new(1))),
+            ValueObj::Imag(i) => Ok(ValueObj::Imag(i + Imag::int_new(1))),
+            ValueObj::Complex(c) => Ok(ValueObj::Complex(c + Complex::int_new(1, 0))),
             ValueObj::Float(n) => Ok(ValueObj::Float(n + f64::EPSILON)),
             ValueObj::Inf | ValueObj::NegInf => Ok(val),
             _ => Err(EvalErrors::from(EvalError::unreachable(
@@ -1410,7 +1413,9 @@ impl Context {
             ValueObj::Bool(_) => Ok(ValueObj::Nat(0)),
             ValueObj::Nat(n) => Ok(ValueObj::Nat(n.saturating_sub(1))),
             ValueObj::Int(n) => Ok(ValueObj::Int(n - 1)),
-            ValueObj::Ratio(r) => Ok(ValueObj::Ratio(r - Ratio::new(1, 1))),
+            ValueObj::Ratio(r) => Ok(ValueObj::Ratio(r - Ratio::int_new(1))),
+            ValueObj::Imag(i) => Ok(ValueObj::Imag(i - Imag::int_new(1))),
+            ValueObj::Complex(c) => Ok(ValueObj::Complex(c - Complex::int_new(1, 0))),
             ValueObj::Float(n) => Ok(ValueObj::Float(n - f64::EPSILON)),
             ValueObj::Inf | ValueObj::NegInf => Ok(val),
             _ => Err(EvalErrors::from(EvalError::unreachable(
diff --git a/crates/erg_compiler/context/instantiate_spec.rs b/crates/erg_compiler/context/instantiate_spec.rs
index c2a6ab550..b5cd2cc0b 100644
--- a/crates/erg_compiler/context/instantiate_spec.rs
+++ b/crates/erg_compiler/context/instantiate_spec.rs
@@ -530,6 +530,8 @@ impl Context {
             "Nat" => Ok(Type::Nat),
             "Int" => Ok(Type::Int),
             "Ratio" => Ok(Type::Ratio),
+            "Imag" => Ok(Type::Imag),
+            "Complex" => Ok(Type::Complex),
             "Float" => Ok(Type::Float),
             "Str" => Ok(Type::Str),
             "Bool" => Ok(Type::Bool),
diff --git a/crates/erg_compiler/ty/value.rs b/crates/erg_compiler/ty/value.rs
index 55b685ced..a25bfef24 100644
--- a/crates/erg_compiler/ty/value.rs
+++ b/crates/erg_compiler/ty/value.rs
@@ -7,17 +7,18 @@ use std::hash::{Hash, Hasher};
 use std::ops::Neg;
 use std::sync::Arc;
 
-use erg_common::dict::Dict;
-use erg_common::error::{ErrorCore, ErrorKind, Location};
 use erg_common::fresh::FRESH_GEN;
-use erg_common::io::Input;
 use erg_common::python_util::PythonVersion;
 use erg_common::ratio::Ratio;
 use erg_common::serialize::*;
 use erg_common::set::Set;
 use erg_common::traits::LimitedDisplay;
-use erg_common::{complex::Complex, config::Input, dict::Dict, imag::Imag};
+use erg_common::{complex::Complex, dict::Dict, imag::Imag};
 use erg_common::{dict, fmt_iter, impl_display_from_debug, log, switch_lang};
+use erg_common::{
+    error::{ErrorCore, ErrorKind, Location},
+    io::Input,
+};
 use erg_common::{ArcArray, Str};
 use erg_parser::ast::{ConstArgs, ConstExpr};
 
@@ -1009,8 +1010,8 @@ impl ValueObj {
         matches!(
             self,
             Self::Float(_)
-                | Self::Ratio(_)
                 | Self::Complex(_)
+                | Self::Ratio(_)
                 | Self::Int(_)
                 | Self::Nat(_)
                 | Self::Bool(_)
@@ -1021,8 +1022,8 @@ impl ValueObj {
         matches!(
             self,
             Self::Float(_)
-                | Self::Ratio(_)
                 | Self::Complex(_)
+                | Self::Ratio(_)
                 | Self::Int(_)
                 | Self::Nat(_)
                 | Self::Bool(_)
@@ -1032,7 +1033,7 @@ impl ValueObj {
     pub const fn is_ratio(&self) -> bool {
         matches!(
             self,
-            Self::Ratio(_) | Self::Complex(_) | Self::Int(_) | Self::Nat(_) | Self::Bool(_)
+            Self::Ratio(_) | Self::Int(_) | Self::Nat(_) | Self::Bool(_)
         )
     }
 
@@ -1347,15 +1348,15 @@ impl ValueObj {
                 Some(Self::Complex(Complex::new(Ratio::new(r as i64, 1), l)))
             }
             (Self::Imag(l), Self::Nat(r)) => {
-                Some(Self::Complex(Complex::new(Ratio::new(r as i64, 1), l)))
+                Some(Self::Complex(Complex::new(Ratio::int_new(r as i64), l)))
             }
             (Self::Ratio(l), Self::Imag(r)) => Some(Self::Complex(Complex::new(l, r))),
             (Self::Int(l), Self::Imag(r)) => {
-                Some(Self::Complex(Complex::new(Ratio::new(l as i64, 1), r)))
+                Some(Self::Complex(Complex::new(Ratio::int_new(l as i64), r)))
             }
             (Self::Nat(l), Self::Imag(r)) => {
                 // TODO: check if l is greater then the max value of i64
-                Some(Self::Complex(Complex::new(Ratio::new(l as i64, 1), r)))
+                Some(Self::Complex(Complex::new(Ratio::int_new(l as i64), r)))
             }
             /* Complex */
             (Self::Complex(l), Self::Complex(r)) => Some(Self::Complex(l + r)),