Math Problem Solver

(I) A carpenter wants to cut three lengths from a single piece of cardboard of length

101cm. The second length is 11 cm longer than the shortest and the third length is

thrice the shortest. What are the possible lengths of the shortest piece, if the third

piece is atleast 8 cm longer than the second?

(II) Following complex numbers are defined as

1

2

3

3 2

3 2

1

z i

z i

z i

 

 

 

Find

(i) = z1 + z2 + z3

(ii) = z1 × z2 × z3

(iii) 1 2

3

2z z

z 

(iv) Represent α, β and γ on a complex plane

(v) Find the Argument and Modulus of α, β and γ.