" 9."((1)/(3)+3i)^(3)

((1)/(3)+3i)^(3)=((1)/(3))^(3)+(3i)^(3)+3(1)/(3))(( 1)/(3)+3i)

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

For the following Aps, write the first term ans the common difference: (i) 3, 1, -1, -3,…………….. (ii) -5, -1, 3, 7,…. (iii) (1)/(3), (5)/(3), (9)/(3), (13)/(3),……………. (iv) 0.6, 1.7, 2.8, 3.9,………

Find a rational number between (i) (3)/(8) and (2)/(5) (ii) 1.3 and 1.4 (iii) - 1 and (1)/(2) (iv) -(3)/(4) and -(2)/(5) (v) (1)/(9) and (2)/(9)

{:("Column A"," ","Column B"),((3cdot 3cdot 3cdot3)/(9 cdot 9 cdot 9 cdot 9),,((1)/(3))^4):}

(1+3i)(1-3i)

[3^(3)(((4)/(9))^((1)/(3))-((2)/(9))^((1)/(3))+((2)/(9))^((1)/(3)))^(-1)-1]^(3)=

Show that ((19 + 9i)/(5 - 3i))^(15) - ((8 + i)/(1 + 2i))^(15) is purely imaginary

Show that ((19+9i)/(5-3i))^(15)-((8+i)/(1+2i))^(15) is purely imaginary.

Without actually calculating the cube find the value of the following : (i) (-9)^(3)+(4)^(3)+(5)^(3) " " (ii) (-18)^(3)+(9)^(3)+(9)^(3) " " (iii) (16)^(3)+(1)^(3)+(-17)^(3) (iv) (8)^(3)+(3)^(3)+(-11)^(3) .