Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box so that the result is as close as possible to the number i.
Hint
What could be done to make a multiplication between a number in polar form and a number in Cartesian form easier?
Which angles for polar form might produce a Cartesian form that has a root in it?
Which angles for polar form might produce a Cartesian form that has a root in it?
Answer
There are two solutions:
4/8 cis( 6/9 pi) ( sqrt(3) – 1i)
2/4 cis( 6/9 pi) ( sqrt(3) – 1i)
4/8 cis( 6/9 pi) ( sqrt(3) – 1i)
2/4 cis( 6/9 pi) ( sqrt(3) – 1i)
Source: David K Butler