Question

Express the given complex number in the form a + ib :

Answer 1

The given complex number is,

( −2− 1 3 i ) 3

On simplifying the given expression, we get

( −2− 1 3 i ) 3 = ( −2 ) 3 + ( − 1 3 i ) 3 +3 ( −2 ) 2 ( − 1 3 i )+3( −2 ) ( − 1 3 i ) 2 =−8− 1 27 i 3 −4i− 2 3 i 2 =−8+ 1 27 i −4i+ 2 3 =− 22 3 +i( − 107 27 )

Therefore, the given expression in the form of a+ib is ( − 22 3 )+i( − 107 27 ).