Question

Express the following complex number in polar form 1/1+i​

Answer 1

Answer:

1/√2 {(cos3π/4+i sin3π/4)}

Step-by-step explanation:

1/1+i = 1-i/(1+i)(1-i) = (1-i)/(1-i²) = (1-i)/(1+1) = (1-i)/2 = 1/2 - i/2

∴ r = √{(1/2)²+(-1/2)²} = √2/4 = 1/√2

∴ Ф = tan^(-1) {(-1/2)/(1/2)}

      = tan^(-1) (-1)

      =  3π/4

Hence, the polar form is = r(cosФ+i sin Ф)

                                        = 1/√2 {(cos3π/4+i sin3π/4)}