If y = 1 i, then y3 - 3y2

Question

Kathryn Dickerson

Mathematics

25 May, 13:46

If y = 1 i, then y3 - 3y2

+1

Answers (2)

Know the Answer?

Ivan Goodwin · Answer 1

Y = 1i = i

y³ - 3y²

(i) ³ - 3 (i) ² i ² = - 1, i³ = i² (i) = - i

i³ - 3i²

-i - 3 (-1)

-i + 3

Noel Bright · Answer 2

Y^3-3y^2

(1+i) ^3-3 (1+i) ^2

remember

(1+i) ^3 = (1+i) (1+i) ^2

(1+i) (1+i) ^2-3 (1+i) ^2

factor out (1+i) ^2

(1+i) ^2 ((1+i) - 3)

(1+i) ^2 (1+i-3)

(1+i) ^2 (i-2)

(1+i) (1+i) (i-2)

(1+2i-1) (i-2)

(2i) (i-2)

-2-4i