How do you divide #-2/i#?

Question

1330 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-24T12:52:49

#(-2)/i=2i#

#i# is a complex number so we can't directly divide by it.

however, we can rationalise the denominator to find another war of expressing it.

#i# can be written as #sqrt(-1)#

so we have,

#(-2)/sqrt(-1)#

#=(-2)/sqrt(-1)*1#

#=(-2)/sqrt(-1)*sqrt(-1)/sqrt(-1)# (multiplying by 1 doesn't change the number)

# =(-2*sqrt(-1))/(sqrt(-1)*sqrt(-1))#

# =(-2*sqrt(-1))/-1#

# =2*sqrt(-1)#

#=2i#

so,

#(-2)/i=2i#

unfortunately, we can determine an actual number as #i# is complex.

Hope this helped.