Question

PLATO:

Find the missing term. If y = 1 + i, then y3 − 3y2 + ( ) − 1 = -i .

Answer 1

X= 6i

Explanation:

We have the following equation:

y^3 - 3y^2 + X - 1 = -i (1),

where X is the missing term.

So, we know that y = 1 + i. Where i = sqrt(-1).

Substituting y = 1 + i in the equation (1):

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

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

Simplifying:

1 + 3i -3i - i - 3(1 + 2i -1) + X - 1 = -i

1 - i -6i + X - 1 = -i

-i - 6i + X = -i

- 6i + X = 0

X= 6i

So the missing term is X= 6i