MATHEMATICAL PROBLEM PAGE Directed by PAUL C. CROSS Gates Chemical Laboratory, California Institute of Technology, Pasadena, California
S
OLUTIONS of the following problems will be given in the May issue. a Giventhat- ( a s + + i s i n + ) = - s i n + + i c o s +
&
where i = (- 1)''.
show that
(ei+ - e-'+)/2i.
+
+
+
+
+
+
.
+
++
=
A complex number x iy, where x and y are real numbers and i = (-I)"', may be represented as a vector in the xy plane from x- r cos # theorigin to the point(x,y). a+bi=c+diifandonlyifa=candb=d, (a bi? * ((G di) = (a * c) (b * d)i.
+
+
+
,w,
+ + i sin + = ei@. Show that cos + = (ei@+ e-
