complex number

Question

express in a+ib form, (1+i)²/3-i

Answer 1

First note that the a+ib form is NOT the polar form of a complex number, but the so-called standard form.

 

When you write (1+i)²/3-i, I'm assuming the -i is not in the denominator, or else you would have put parentheses, (3-i).

 

Square out (1+i)²,

 

(1+i)²=2i,

 

divide by 3 and subtract i:

 

(1+i)²/3 - i = 2i/3 - i = (2/3 - 1) i = -1/3 i