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

If |x pi| le 1, A = 1/pi [(sin^-1(xpi), tan^-1(x/pi)),(sin^-1(x/pi) ,cot^-1(xpi))] and B = 1/pi[(-cos^-1(xpi), tan^-1(x/pi)),(sin^-1(x/pi) , -tan^-1(xpi))] then A - B is equal to

If z=(i) ^((i) ^(i)) where i= sqrt (−1) ​ , then z is equal to

The possible values of theta in (0,pi) such that sin (theta) + sin (4theta) + sin(7theta) = 0 are (1) (2pi)/9 , i/4 , (4pi)/9, pi/2, (3pi)/4 , (8pi)/9 (2) pi/4, (5pi)/12, pi/2 , (2pi)/3, (3pi)/4, (8pi)/9 (3) (2pi)/9, pi/4 , pi/2 , (2pi)/3 , (3pi)/4 , (35pi)/36 (4) (2pi)/9, pi/4, pi/2 , (2pi)/3 , (3pi)/4 , (8pi)/9

For f(x) =x^(4) +|x|, let I_(1)= int _(0)^(pi)f(cos x) dx and I_(2)= int_(0)^(pi//2) f(sin x ) dx "then" (I_(1))/(I_(2)) has the value equal to

If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0 , where i=sqrt(-1) , then z bar(z) is equal to

The value of (1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)i s (a)1/4 (b) 3/4 (c) 1/8 (d) 3/8

If z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Find the value of Im(z) .

tan^(-1)[sin(-pi/2)]=pi/4 .

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then z 1 ​ +z 2 ​ is equal to

If arg (z_(1))=(17pi)/18 and arg (z_(2))=(7pi)/18, find the principal argument of z_(1)z_(2) and (z_(1)//z_(2)).