" (ii) "(i-2)^(2)

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)) .

Show that (2-i)/((1-2i)^(2)) and ((-2-11 i)/(25)) are conjugate to each other

Find the following |(i(1+2i)^(2))/((2+i)^4)|

Find the conjugate of ((1-2i)^(2))/(2 + i)

Find the conjugate of ((1-2i)^(2))/(2 + i)

If z=x+iy is a complex number satisfying |z+(i)/(2)|^(2)=|z-(i)/(2)|^(2), then the locus of z is

a+ib: (1)/((2+i)^(2))-(1)/((2-i)^(2))

If 1 is the incentre and I_1,I_2,I_3 are the centre of escribed circles of the triangleABC . Prove that II_(1)^(2)+I_2I_(3)^(2)= II_(2)^(2)+I_(3)I_(1)^(2)= I_(1)I_(2)^(2)+II_(3)^(2)