QuestionJuly 15, 2025

Select the correct answer from each drop-down menu. Find the missing term. If y=1+i then y^3-3y^2+(square )-1=-1

Select the correct answer from each drop-down menu. Find the missing term. If y=1+i then y^3-3y^2+(square )-1=-1
Select the correct answer from each drop-down menu. Find the missing term. If y=1+i then y^3-3y^2+(square )-1=-1

Solution
4.5(286 votes)

Answer

2 + 4i Explanation 1. Simplify the given expression Substitute y = 1 + i into y^3 - 3y^2 + (\square) - 1 = -1. 2. Calculate y^2 y^2 = (1+i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i. 3. Calculate y^3 y^3 = y \cdot y^2 = (1+i)(2i) = 2i + 2i^2 = 2i - 2 = -2 + 2i. 4. Substitute and solve for the missing term Substitute y^3 = -2 + 2i and y^2 = 2i into the equation: (-2 + 2i) - 3(2i) + (\square) - 1 = -1. Simplify: -2 + 2i - 6i + (\square) - 1 = -1. Combine like terms: -3 - 4i + (\square) = -1. Solve for (\square): (\square) = -1 + 3 + 4i = 2 + 4i.

Explanation

1. Simplify the given expression<br /> Substitute $y = 1 + i$ into $y^3 - 3y^2 + (\square) - 1 = -1$.<br /><br />2. Calculate $y^2$<br /> $y^2 = (1+i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i$.<br /><br />3. Calculate $y^3$<br /> $y^3 = y \cdot y^2 = (1+i)(2i) = 2i + 2i^2 = 2i - 2 = -2 + 2i$.<br /><br />4. Substitute and solve for the missing term<br /> Substitute $y^3 = -2 + 2i$ and $y^2 = 2i$ into the equation:<br /> $(-2 + 2i) - 3(2i) + (\square) - 1 = -1$.<br /> Simplify: $-2 + 2i - 6i + (\square) - 1 = -1$.<br /> Combine like terms: $-3 - 4i + (\square) = -1$.<br /> Solve for $(\square)$: $(\square) = -1 + 3 + 4i = 2 + 4i$.
Click to rate:

Similar Questions