Express 1/(1 + 1/(1 + i)) in the form a + bi, where a and b are real numbers.
+23245 First: simplify 1 / (1 + i) by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of 1 + i is 1 - i.
1 / (1 + i) x (1 - i) / (1 - i) = (1 - i) / 2
You now have: 1 / ( 1 + (1 - i) / 2 ) = 1 / ( 1 + 1/2 - i/2 ) = 1 / ( 3/2 - i/2 )
Simplify by multiplying both the numerator and denominator by the conjugate of the denominator.
1 / ( 3/2 - i/2 ) x ( 3/2 + i/2 ) / ( 3/2 + i/2 ) = (3/2 + i/2) / 2.5 = 0.6 + 0.2i
