diff --git a/collects/tests/typed-racket/optimizer/tests/unboxed-exp.rkt b/collects/tests/typed-racket/optimizer/tests/unboxed-exp.rkt
new file mode 100644
index 0000000000..09e07d8d6a
--- /dev/null
+++ b/collects/tests/typed-racket/optimizer/tests/unboxed-exp.rkt
@@ -0,0 +1,27 @@
+#;
+(
+TR opt: unboxed-exp.rkt 23:5 2.0+3.4i -- unboxed literal
+TR opt: unboxed-exp.rkt 23:0 (exp 2.0+3.4i) -- unboxed unary float complex
+TR opt: unboxed-exp.rkt 24:5 0.0+0.0i -- unboxed literal
+TR opt: unboxed-exp.rkt 24:0 (exp 0.0+0.0i) -- unboxed unary float complex
+TR opt: unboxed-exp.rkt 25:5 -12.2-4.7i -- unboxed literal
+TR opt: unboxed-exp.rkt 25:0 (exp -12.2-4.7i) -- unboxed unary float complex
+TR opt: unboxed-exp.rkt 26:5 12.2-4.7i -- unboxed literal
+TR opt: unboxed-exp.rkt 26:0 (exp 12.2-4.7i) -- unboxed unary float complex
+TR opt: unboxed-exp.rkt 27:5 -12.2+4.7i -- unboxed literal
+TR opt: unboxed-exp.rkt 27:0 (exp -12.2+4.7i) -- unboxed unary float complex
+-7.143726081314396-1.8882075384588168i
+1.0+0.0i
+-6.232062158151458e-08+5.030069557694479e-06i
+-2462.731893583747+198773.89557926523i
+-6.232062158151458e-08-5.030069557694479e-06i
+)
+
+#lang typed/racket
+#:optimize
+
+(exp 2.0+3.4i)
+(exp 0.0+0.0i)
+(exp -12.2-4.7i)
+(exp 12.2-4.7i)
+(exp -12.2+4.7i)
diff --git a/collects/typed-racket/optimizer/float-complex.rkt b/collects/typed-racket/optimizer/float-complex.rkt
index 283943ee5f..0ce34696ea 100644
--- a/collects/typed-racket/optimizer/float-complex.rkt
+++ b/collects/typed-racket/optimizer/float-complex.rkt
@@ -246,6 +246,20 @@
                                       (unsafe-fl+ (unsafe-fl* c.real-binding c.real-binding)
                                                   (unsafe-fl* c.imag-binding c.imag-binding)))))))
 
+  (pattern (#%plain-app (~and op (~literal exp)) c:unboxed-float-complex-opt-expr)
+           #:with real-binding (unboxed-gensym "unboxed-real-")
+           #:with imag-binding (unboxed-gensym "unboxed-imag-")
+           #:with scaling-factor (unboxed-gensym "unboxed-scaling-")
+           #:with (bindings ...)
+           (begin (log-optimization "unboxed unary float complex"
+                                    complex-unboxing-opt-msg
+                                    this-syntax)
+                  (add-disappeared-use #'op)
+                  #`(c.bindings ...
+                     ((scaling-factor) (unsafe-flexp c.real-binding))
+                     ((real-binding)   (unsafe-fl* (unsafe-flcos c.imag-binding) scaling-factor))
+                     ((imag-binding)   (unsafe-fl* (unsafe-flsin c.imag-binding) scaling-factor)))))
+
   (pattern (#%plain-app (~and op (~or (~literal real-part) (~literal unsafe-flreal-part)))
                         c:unboxed-float-complex-opt-expr)
            #:with real-binding #'c.real-binding
@@ -398,7 +412,7 @@
 
 (define-syntax-class float-complex-op
   #:commit
-  (pattern (~or (~literal +) (~literal -) (~literal *) (~literal /) (~literal conjugate))))
+  (pattern (~or (~literal +) (~literal -) (~literal *) (~literal /) (~literal conjugate) (~literal exp))))
 
 (define-syntax-class float-complex->float-op
   #:commit