("vii")2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)

Write the following in the form x+iy: (i) (3+2i)(2-i) (ii) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25) . (iii) ((3-2i)(2+3i))/((1+2i)(2-i)) .

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 .

Evaluate 2i^(2)+ 6i^(3)+3i^(16) -6i^(19) + 4i^(25)

Evaluate 2i^(2)+ 6i^(3)+3i^(16) -6i^(19) + 4i^(25)

simplify the following 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)

If 2i^2+6i^3+3i^(16)-6i^(19)+4i^(25)=x+iy , then

Simplify: 2i^2+6i^3+3i^16-6i^19+4i^25

Prove that : 2i^2+6i^3+3i^16-6i^19+4i^25=1+4i .

Evaluate: (i^(2)+i^(4)+i^(6)+i^(7))/(1+i^(2)+i^(3))

Simplify the following : (i) [i^(19) +(1)/(i^(25))]^(2) (ii) [i^(5)- (1)/(i^(3))]^(4)