Question

Which of the following is standard i/1-1?
a) 1-i
b) -1/2 -1/2
c)1+i
d) 1/2 + 1/2i

Answer 1

Sorry, typo - I'll take a screen shot

Answer 2

See attachment for standard form of a complex number

Answer 3

Samples

Answer 4

Option D is correct. Before you can make a selection from the options, you have to work with the given number. The work shown on the attachment you posted is correct.

Answer 5

Okay I was a little confused by the work in the explanation - are they just multiplying the top and bottom by (1-i)?

Answer 6

I mean (1+i) ...

Answer 7

yes, it is a "trick" to multiply by the *complex conjugate*
if you have
a+bi then a-bi is the conjugate
if you have
a-bi then a+bi is the conjugate

Answer 8

the idea is if you multiply the bottom by its complex conjugate, you get a real number
to keep things equal you have to also multiply the top by the same thing

Answer 9

This makes sense - thanks guys!

Answer 10

Of course you have to know how to multiply to complex numbers
for the special case
(a+bi)(a-bi) and using FOIL (do as in multiplying binomials if you know how to do that)
you get
a*a + abi + -abi - i^2 b^2
the middle part cancels
-i*i turns into +1
and it boils down to
a^2 + b^2

so you if see
(5+6i)(5-6i)
you could by rote write it as : 5^2 + 6^2