The polar form of the complex number z = 1 1 + i , (where i = -1 ) is

Step-by-step solution

z = 1 1 + i Multiplying the numerator and denominator by the conjugate of the denominator: z = 1(1 - i) (1 + i)(1 - i) = 1 - i 1^2 - i^2 = 1 - i 2 = 1 2 - 1 2 i The modulus of z is: r = |z| = ( 1 2 )^2 + (- 1 2 )^2 = 1 4 + 1 4 = 1 2 = 1 2 The argument of z is: = ⁻¹ ( -1/2 1/2 ) = ⁻¹(-1) Since z lies in the fourth quadrant, = 2 - 4 = 7 4 . Thus, the polar form of z is: z = r( + i ) = 1 2 ( 7 4 + i 7 4 ) Answer: 1 2 ( 7 4 + i 7 4 )