Question

express the following complex number in the standard form a+ib:​

Answer 1

Answer:

-$\sqrt{3}$ +i

Step-by-step explanation:

[ (1+i) ( 1+$\sqrt{3}$i) ] / (1-i)

= [ (1+i) ( 1+$\sqrt{3}$i) ] / (1-i)  x (1+i)*(1-i)

=  [ (1+i)² ( 1+$\sqrt{3}$i) ] / (1²-i²)

=  [ (1²+2(1)(i)+i²) ( 1+$\sqrt{3}$i) ] / (1-(-1))

=  [ (1+2i+(-1)) ( 1+$\sqrt{3}$i) ] / (1+1))

=  [ (2i) ( 1+$\sqrt{3}$i) ] / 2)

= (i) ( 1+$\sqrt{3}$i)

= ( i(1) +  $\sqrt{3}$i(i) )

= -$\sqrt{3}$ +i