The conjugate of the multiplicative inverse of the complex number z = 1 + 7i 3 + i is:

Step-by-step solution

z = 1 + 7i 3 + i Multiplying the numerator and denominator by the conjugate of the denominator: z = (1 + 7i)(3 - i) (3 + i)(3 - i) z = 3 - i + 21i - 7i^2 3^2 - i^2 z = 3 + 20i + 7 9 + 1 z = 10 + 20i 10 = 1 + 2i The multiplicative inverse of z is 1 z : 1 z = 1 1 + 2i 1 z = 1 - 2i (1 + 2i)(1 - 2i) 1 z = 1 - 2i 1^2 + 2^2 = 1 5 - 2 5 i The conjugate of the multiplicative inverse is: ( 1 z ) = 1 5 + 2 5 i Answer: 1 5 + 2 5 i