[" 27.If "(sqrt(3)+i)/(2)=(a+i)/(a-i)" and "a" is a real number,then "],[" find the value of "a" ."]

If (sqrt(3)+i)/(2)=(a+i)/(a-i) and a is a real number, then a is

Prove that (3+i)/(1+2i)+(3-i)/(1-2i) is a real number.

Prove that (3+i)/(1+2i)+(3-i)/(1-2i) is a real number.

If 3i^(3)-2ai^(2)+(1-a)i+5 is real then find the value of a.

If i=sqrt(-1), and ((7+5i))/((-2-6i))=a+bi , where a and b are real numbers, then what is the value of |a+b| ?

Show that (-1+sqrt3 i)^3 is a real number

Let z=(11-3i)/(1+i) . If alpha is a real number such z-ialpha is real, then the value of alpha is

Show that (-1+sqrt(-3i))^3 is a real number

(Show that (-1+sqrt(3)i)^(3) is a real number

If (2+i)/(2-3i)=A+iB (A,B" ""are real", i =sqrt(-1)), find the value of A^(2)+B^(2)