`(1+i)^(8)+(1-i)^(8)=`

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

Express the following in the form of a + b i :(i) (-5i)(1/8i) (ii) (-i)(2i)(-1/8i)^3

Solve the following equations: (i) sin^(8)x - cos^(8)x=1 (ii) sin^(10)x - cot^(8)x=1

Principle Argument of z=(2+i)/((1+i)^(200)(1-2i)) is 1 dot-pi/4 2. pi/8 3. -pi/2 4. pi/4 5. pi/2

Show that (i) sin^(8)A-cos^(8)A=(sin^(2)A-cos^(2)A)(1-2sin^(2)A.cos^(2)A) (ii) (1)/(sec A-tan A)-(1)/(cos A)=(1)/(cos A)-(1)/(sec A + tan A)

If sum_(i=1)^(18)(x_(i) - 8) = 9 and sum_(i=1)^(18)(x_(i) - 8)^(2) = 45 then find the standard deviation of x_(1), x_(2),….x_(18)

Simplify (i) {(1/3)^(-2) - (1/2)^(-3)} -: (1/4)^(-2). (ii) (5/8)^(-7) xx (8/5)^(-5).

Factorise : (i) 125a^(3)+(1)/(8) " " (ii) 8a^(3)-27b^(3)

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)

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1)^(2)| = |z_(2)|^(2)