[" EXERCISE "5.2],[" (iii) "(1+i)^(4)(1+(1)/(i))^(4)]

((1+i)/(1-i))^(4)+((1-i)/(1+i))^(4)=

((1+i)/(1-i))^4+((1-i)/(1+i))^4=

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 .

Simplify the following : (i) 1+ i^(5)+i^(10)+i^(15) (ii) (1+i)^(4)+(1+(1)/(i))^(4) (iii) i^(n)+i^(n+1)+i^(n+2)+i^(n+3)

Simplify the following : (i) 1+ i^(5)+i^(10)+i^(15) (ii) (1+i)^(4)+(1+(1)/(i))^(4) (iii) i^(n)+i^(n+1)+i^(n+2)+i^(n+3)

Simplify : (i)" "(-2i)((1)/(6)i)" "(ii)" "(-i)(3i)((-1)/(6)i)^(3)" "(iii)" "4 sqrt(-4)+5 sqrt(-9)-3 sqrt(-16)

Convert the following in the form of (a+ib) : (i) (1+i)^(4) (ii) (-3+(1)/(2)i)^(3) (iii) (1-i)(3+4i) (iv) (1+i)(1+ 2i)(1+ 3i) (v) (3+5i)/(6-i) (vi) ((2+3i)^(2))/(2+i) (vii) ((1+ i)(2+i))/((3+i)) (viii) (2-i)^(-3)

Convert the following in the form of (a+ib) : (i) (1+i)^(4) (ii) (-3+(1)/(2)i)^(3) (iii) (1-i)(3+4i) (iv) (1+i)(1+ 2i)(1+ 3i) (v) (3+5i)/(6-i) (vi) ((2+3i)^(2))/(2+i) (vii) ((1+ i)(2+i))/((3+i)) (viii) (2-i)^(-3)

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