`{i^(17)-(1/i)^(34)}^2`

Evaluate [ i^(14) - (1/i)^(34)]^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 .

Evaluate (i^17-1/i^34)^3 .

[i^(17)+1/(i^(315))]^(9) is equal to

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

If z=((sqrt(3)+i)^(17))/((1-i)^(50)), then find amp(z)

Show that 6i^(50)+5i^(17)-i^(11)+6i^(28) is an imaginary number.

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)

((12)/(17)times(12)/(17)-(13)/(34)times(13)/(34))/((12)/(17)+(13)/(34))

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)