diff --git a/collects/tests/typed-scheme/optimizer/generic/inexact-complex-conjugate.rkt b/collects/tests/typed-scheme/optimizer/generic/inexact-complex-conjugate.rkt
new file mode 100644
index 0000000000..9c647f6ab6
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/generic/inexact-complex-conjugate.rkt
@@ -0,0 +1,3 @@
+#lang typed/scheme #:optimize
+(require racket/unsafe/ops)
+(+ (conjugate 1.0+2.0i) (conjugate 2.0+4.0i))
diff --git a/collects/tests/typed-scheme/optimizer/hand-optimized/inexact-complex-conjugate.rkt b/collects/tests/typed-scheme/optimizer/hand-optimized/inexact-complex-conjugate.rkt
new file mode 100644
index 0000000000..e5bc9583bc
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/hand-optimized/inexact-complex-conjugate.rkt
@@ -0,0 +1,13 @@
+#lang typed/scheme #:optimize
+(require racket/unsafe/ops)
+(let* ((unboxed-gensym-1 1.0+2.0i)
+       (unboxed-gensym-2 (unsafe-flreal-part unboxed-gensym-1))
+       (unboxed-gensym-3 (unsafe-flimag-part unboxed-gensym-1))
+       (unboxed-gensym-4 (unsafe-fl- 0.0 unboxed-gensym-3))
+       (unboxed-gensym-5 2.0+4.0i)
+       (unboxed-gensym-6 (unsafe-flreal-part unboxed-gensym-5))
+       (unboxed-gensym-7 (unsafe-flimag-part unboxed-gensym-5))
+       (unboxed-gensym-8 (unsafe-fl- 0.0 unboxed-gensym-7))
+       (unboxed-gensym-9 (unsafe-fl+ unboxed-gensym-2 unboxed-gensym-6))
+       (unboxed-gensym-10 (unsafe-fl+ unboxed-gensym-4 unboxed-gensym-8)))
+  (unsafe-make-flrectangular unboxed-gensym-9 unboxed-gensym-10))
diff --git a/collects/typed-scheme/optimizer/inexact-complex.rkt b/collects/typed-scheme/optimizer/inexact-complex.rkt
index bdaaadc32e..a386545082 100644
--- a/collects/typed-scheme/optimizer/inexact-complex.rkt
+++ b/collects/typed-scheme/optimizer/inexact-complex.rkt
@@ -2,7 +2,7 @@
 
 (require syntax/parse
          "../utils/utils.rkt"
-         (for-template scheme/base scheme/flonum scheme/unsafe/ops)
+         (for-template scheme/base scheme/math scheme/flonum scheme/unsafe/ops)
          (types abbrev type-table utils subtype)
          (optimizer utils float))
 
@@ -104,6 +104,13 @@
                                                                       (unsafe-fl* #,o2 #,(car e2)))
                                                           #,(car d)))
                                            res)))))))
+  (pattern (#%plain-app (~and op (~literal conjugate)) c:unboxed-inexact-complex-opt-expr)
+           #:with real-part #'c.real-part
+           #:with imag-part (unboxed-gensym)
+           #:with (bindings ...)
+           (begin (log-optimization "unboxed unary inexact complex" #'op)
+                  #`(#,@(append (syntax->list #'(c.bindings ...))
+                                (list #'(imag-part (unsafe-fl- 0.0 c.imag-part)))))))
   (pattern e:expr
            ;; can't work on inexact reals, which are a subtype of inexact
            ;; complexes, so this has to be equality