diff --git a/Sources/Complex/Complex.swift b/Sources/Complex/Complex.swift
index f888014c..00fe5ca0 100644
--- a/Sources/Complex/Complex.swift
+++ b/Sources/Complex/Complex.swift
@@ -2,7 +2,7 @@
 //
 // This source file is part of the Swift Numerics open source project
 //
-// Copyright (c) 2019 Apple Inc. and the Swift Numerics project authors
+// Copyright (c) 2019 - 2020 Apple Inc. and the Swift Numerics project authors
 // Licensed under Apache License v2.0 with Runtime Library Exception
 //
 // See https://swift.org/LICENSE.txt for license information
@@ -344,11 +344,23 @@ extension Complex: Hashable {
 }
 
 // MARK: - Conformance to Codable
-// The synthesized conformance works correction for this protocol, unlike
-// Hashable and Equatable; all we need to do is specify that we conform.
 // FloatingPoint does not refine Codable, so this is a conditional conformance.
-extension Complex: Encodable where RealType: Encodable { }
-extension Complex: Decodable where RealType: Decodable { }
+extension Complex: Decodable where RealType: Decodable {
+  public init(from decoder: Decoder) throws {
+    var unkeyedContainer = try decoder.unkeyedContainer()
+    let x = try unkeyedContainer.decode(RealType.self)
+    let y = try unkeyedContainer.decode(RealType.self)
+    self.init(x, y)
+  }
+}
+
+extension Complex: Encodable where RealType: Encodable {
+  public func encode(to encoder: Encoder) throws {
+    var unkeyedContainer = encoder.unkeyedContainer()
+    try unkeyedContainer.encode(x)
+    try unkeyedContainer.encode(y)
+  }
+}
 
 // MARK: - Formatting
 extension Complex: CustomStringConvertible {
diff --git a/Tests/ComplexTests/PropertyTests.swift b/Tests/ComplexTests/PropertyTests.swift
index 475fd279..6c21791a 100644
--- a/Tests/ComplexTests/PropertyTests.swift
+++ b/Tests/ComplexTests/PropertyTests.swift
@@ -2,7 +2,7 @@
 //
 // This source file is part of the Swift Numerics open source project
 //
-// Copyright (c) 2019 Apple Inc. and the Swift Numerics project authors
+// Copyright (c) 2019 - 2020 Apple Inc. and the Swift Numerics project authors
 // Licensed under Apache License v2.0 with Runtime Library Exception
 //
 // See https://swift.org/LICENSE.txt for license information
@@ -102,4 +102,31 @@ final class PropertyTests: XCTestCase {
     testEquatableHashable(Float80.self)
     #endif
   }
+
+  func testCodable<T: Codable & Real>(_ type: T.Type) throws {
+    let encoder = JSONEncoder()
+    encoder.nonConformingFloatEncodingStrategy = .convertToString(
+      positiveInfinity: "inf",
+      negativeInfinity: "-inf",
+      nan: "nan")
+
+    let decoder = JSONDecoder()
+    decoder.nonConformingFloatDecodingStrategy = .convertFromString(
+      positiveInfinity: "inf",
+      negativeInfinity: "-inf",
+      nan: "nan")
+
+    for expected: Complex<T> in [.zero, .one, .i, .infinity] {
+      let data = try encoder.encode(expected)
+      // print("*** \(String(decoding: data, as: Unicode.UTF8.self)) ***")
+      let actual = try decoder.decode(Complex<T>.self, from: data)
+      XCTAssertEqual(actual, expected)
+    }
+  }
+
+  func testCodable() throws {
+    try testCodable(Float32.self)
+    try testCodable(Float64.self)
+    // Float80 doesn't conform to Codable.
+  }
 }