[" (iv)(1+i) "^(4)(1+(1)/(i))^(4)=16],[" 1"*lm z_(2)]

Prove that: (i) (1-i)^(2)=-2i (ii) (1+i)^(4)xx(1+(1)/(i))^(4)=16 (iii) {i^(19)+((1)/(i))^(25)}^(2)=-4 (iv) i^(4n)+i^(4n+1)+i^(4n+2)+i^(4n+3)=0 (v) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)=1+4i .

Prove that (1+i)^4(1+1/i)^4=16

Prove that : (1+i)^4 xx(1+1/i)^4=16 .

If Z_(1)=2 + 3i and z_(2) = -1 + 2i then find (i) z_(1) +z_(2) (ii) z_(1) -z_(2) (iii) z_(1).z_(2) (iv) z_(1)/z_(2)

If Z_(1)=2 + 3i and z_(2) = -1 + 2i then find (i) z_(1) +z_(2) (ii) z_(1) -z_(2) (iii) z_(1).z_(2) (iv) z_(1)/z_(2)

The descending order of the moduli of z_(1) = (3 - 4i) (4 + 3i) , z_(2) = (3 + 4i)/(1 +i) , z_(3) = ((3 + i) (2- i))/(1+ i) , z_(4) = 5 + 12 i is

If z_(1) =3 -4i and z_(2) = 5 + 7i ,verify (i) |-z_(1)| =|z_(1)| (ii) |z_(1) +z_(2)| lt |z_(2)|

If z_(1) =3 -4i and z_(2) = 5 + 7i ,verify (i) |-z_(1)| =|z_(1)| (ii) |z_(1) +z_(2)| lt |z_(2)|

If z_(k)=e^(i theta_k) for k= 1, 2, 3, 4 where i^(2)= -1 , and if |sum_(k=1)^(4) (1)/(z_k)|=1 , then |sum_(k=1)^(4)| is equal to