Question

Write the complex number 1 +i/1 -i into polar form​

Answer 1

cos(pi/2) + i sin (pi/2)

Explanation:

(1+i)/ (1-i)

Multiply top and bottom by (1+i)

(1+i) (1+i)/ (1-i)(1+i)

Foil the top (1+i)(1+i) = 1 +2i +i^2 = 1 +2i -1 = 2i

Foil the bottom ( 1+i)(1-i) = 1 - i^2 = 1 - (-1) =2

2i/2 = i

the magnitude is (0^2+1^2) = 1

The angle is tan^-1( 1/0) = pi/2

cos(pi/2) + i sin (pi/2)