# Let z = (11-3i)/(1+i). If a is real number such that z-ia is real, then the value of a is (1) 4 (2) -4 (3) 7 (4) -7

Solution:

Given z = (11-3i)/(1+i)

Multiply numerator and denominator with (1-i)

z = (11-3i)(1-i)/(1+i)(1-i)

= (11-3i-11i-3)/(1+1)

= (8-14i)/2

= 4-7i

z-ia = 4-7i-ia

z-ia real means imaginary part is zero.

-7-a = 0

a = -7

Hence option (4) is the answer.