diff --git a/typed-racket-lib/typed-racket/optimizer/float-complex.rkt b/typed-racket-lib/typed-racket/optimizer/float-complex.rkt
index 68d84521..8a670e31 100644
--- a/typed-racket-lib/typed-racket/optimizer/float-complex.rkt
+++ b/typed-racket-lib/typed-racket/optimizer/float-complex.rkt
@@ -565,9 +565,11 @@
           [(#%plain-app op:magnitude^ c:unboxed-float-complex-opt-expr)
            (log-unboxing-opt "unboxed unary float complex")
            #`(let*-values (c.bindings ...)
-               (unsafe-flsqrt
-                 (unsafe-fl+ (unsafe-fl* c.real-binding c.real-binding)
-                             (unsafe-fl* c.imag-binding c.imag-binding))))])))
+               ;; reuses the algorithm used by the Racket runtime
+               (let-values ([(q) (unsafe-fl/ c.real-binding c.imag-binding)])
+                 (unsafe-fl* c.imag-binding
+                             (unsafe-flsqrt (unsafe-fl+ 1.0
+                                                        (unsafe-fl* q q))))))])))
 
 
   (pattern (#%plain-app op:float-complex-op e:expr ...)
diff --git a/typed-racket-test/optimizer/known-bugs.rkt b/typed-racket-test/optimizer/known-bugs.rkt
index d85c35cb..5919c734 100644
--- a/typed-racket-test/optimizer/known-bugs.rkt
+++ b/typed-racket-test/optimizer/known-bugs.rkt
@@ -85,7 +85,7 @@
     (good-opt (+ (expt 10 501) (expt -10 501) 1.0+1.0i))
 
     ;; Magnitude should not overflow unless necessary
-    (bad-opt (magnitude 3.0e300+4.0e300i))
+    (good-opt (magnitude 3.0e300+4.0e300i))
 
     ;; Negation should correctly compute sign of 0.0
     (good-opt (- 0.0+0.0i))