diff --git a/typed-racket-lib/typed-racket/optimizer/float-complex.rkt b/typed-racket-lib/typed-racket/optimizer/float-complex.rkt
index 529aa655..88f9835c 100644
--- a/typed-racket-lib/typed-racket/optimizer/float-complex.rkt
+++ b/typed-racket-lib/typed-racket/optimizer/float-complex.rkt
@@ -570,11 +570,18 @@
            #`(let*-values (c.bindings ...)
                ;; reuses the algorithm used by the Racket runtime
                (let*-values ([(r) (unsafe-flabs c.real-binding)]
-                             [(i) (unsafe-flabs c.imag-binding)]
-                             [(q) (unsafe-fl/ r i)])
-                 (unsafe-fl* i
-                             (unsafe-flsqrt (unsafe-fl+ 1.0
-                                                        (unsafe-fl* q q))))))])))
+                             [(i) (unsafe-flabs c.imag-binding)])
+                 (if (zero? i)
+                     r
+                     (if (unsafe-fl< i r)
+                         (let-values ([(q) (unsafe-fl/ i r)])
+                           (unsafe-fl* r
+                                       (unsafe-flsqrt (unsafe-fl+ 1.0
+                                                                  (unsafe-fl* q q)))))
+                         (let-values ([(q) (unsafe-fl/ r i)])
+                           (unsafe-fl* i
+                                       (unsafe-flsqrt (unsafe-fl+ 1.0
+                                                                  (unsafe-fl* q q)))))))))])))
 
 
   (pattern (#%plain-app op:float-complex-op e:expr ...)