Question 713376
Express each complex number in the form a + bi
1) {{{ sqrt(-12)-sqrt(-48) }}}
No i term.
---------------
2) {{{ (3-2i)^2 }}}
Use FOIL as usual
= {{{3^2 - 12i + 4i^2}}}
= {{{9 - 12i - 4}}}
= 5 - 12i
-------------
3) {{{ 1/(4-7i) }}}
Multiply NUM and DEN by the conjugate of the DEN (4+7i)
= {{{(4+7i)/(4^2 - (7i)^2)}}}
= {{{4+7i)/(16 + 49)
= (4+7i)/65
or (4/65) + (7/65)i
-----------------
4) {{{ (sqrt(3)+2i)/(sqrt(3)-2i) }}}
Same as #3
-----------------
5) 4(3+4i) - 5i(1+i)
Simple
-----------
6) {{{ i^23 }}} 
= {{{i^20*i^3}}}
= {{{i^2*i}}}
= -i