Homework SourseShow that 1i iSolutionIn general for real numbers a and b w
Show that 1/i = -i.
Solution
In general, for real numbers a and b where at least one of either a or b is nonzero,
1/(a + bi) = (a - bi)/(a^2 + b^2).
You can see that the above forumla works by multiplying both sides by (a + bi).
1 = (a + bi)(a - bi)/(a^2 + b^2) = (a^2 + b^2)/(a^2 + b^2) = 1.
In your specific example,
1/i = 1/(0 + 1i) = (0 - 1i)/(0^2 + 1^2) = -i/1 = -i.
Hence proved
