`i^(12)+i^(13)+i^(14)+i^(15)`

Write the following in the form x+iy: (i) i+i^(2)+i^(3)+i^(4) (ii) i^(4)+i^(8)+i^(12)+i^(16) (iii) i+i^(5)+i^(9)+i^(13) (iv) i^(9)+i^(10)+i^(11)+i^(12) .

Show that i^(15)+i^(17)+i^(19)+i^(21)+i^(24) is a real number.

Find the values of the following : (i) i^(7)+i^(17)+i^(12) (ii) i^(11)+i^(-11) (iii) i^(3)+(1)/(i^(3)) (iv) 1+i^(2)+i^(6)+i^(8)

Write the following in the form x+iy: i^(9)+i^(10)+i^(11)+i^(12) .

Simplify the following: i^(4)+i^(8)+i^(12)+i^(16)

6i^(50) + 5i^(33) - 2i^(15) + 6i^(48) = 7i .

Simplify the following : (i) i^(97) (ii) i^(8) (iii) (1)/(i^(3)) (iv) (-i)^(14) (v) i^(-22) (vi) i^(-63)