If `z=pi/4(1+i)^4((1-sqrt(pi)i)/(sqrt(pi)+i)+(sqrt(pi)-i)/(1+sqrt(pi)i)),then"((|z|)/(a m p(z)))` equal

If z(2-2sqrt(3i))^2=i(sqrt(3)+i)^4, then a r g(z)=

The complex number, z=((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))

If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)dot

For z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i)) , z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i)) , prove that |z_(1)|=|z_(2)|=|z_(3)|

If z=(sqrt(3)-i)/2 , where i=sqrt(-1) , then (i^(101)+z^(101))^(103) equals to

lim_(xrarr1^(-)) (sqrtpi-sqrt(2sin^-1x))/sqrt(1-x)= (A) sqrt(2/pi) (B) sqrt(pi/2) (C) 1/pi (D) sqrt(1/pi)

If |z_(1)| = sqrt(2), |z_(2)| = sqrt(3) and |z_(1) + z_(2)| = sqrt((5-2sqrt(3))) then arg ((z_(1))/(z_(2))) (not neccessarily principal) is (a) (3pi)/(4) (b) (2pi)/(3) (c) (5pi)/(4) (d) (5pi)/(2)

If z = (sqrt(3+i))/2 (where i = sqrt(-1) ) then (z^101 + i^103)^105 is equal to

If z = (-4 +2 sqrt3i)/(5 +sqrt3i) , then the value of arg(z) is

If i=sqrt(-1) , then (i^(n)+i^(-n), n in Z) is equal to