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

Write the comple number in a + ib form unsing cube roots of unity: (a) (-(1)/(2) + sqrt(3)/(2)i)^(1000) (b)If z =(sqrt(3) + i)^(17)/((1-i)^(50)) (c) (i + sqrt(3))^(100) + (i+ sqrt(3))^(100) + 2^(100)

If z(2-2sqrt(3i))^(2)=i(sqrt(3)+i)^(4), then arg(z)=

If z(2-i2sqrt(3))^(2)=i(sqrt(3)+i)^(4), then amplitude of z is

If z = (sqrt(5)+3i) , find z^(-1) .

If z=(1)/(2)(i sqrt(3)-1), then find the value of (z-z^(2)+2z^(3))(2-z+z^(2))

If z=(1-i)^(6)+(1-i) , then find the modulus of z (i.e., |z|) and multiplicative inverse of z (i.e., z^(-1) ).

If z = frac((1+i)(1+sqrt3i)^2)(1-i) , find |z| , arg z and barz .

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