Question

If x=3i, y=2i, and z=(m+i), and i= square root of -1 then the expression xy²z=?

Answer 1

The expression xy²z given x=3i, y=2i, and z=(m+i) simplifies to -12im + 12. The calculation utilizes the property of i being the square root of -1 and basic algebraic manipulation.

Step-by-step explanation:

The question involves complex numbers and basic algebraic manipulation. Given x=3i, y=2i, and z=(m+i), where i is the square root of -1, we are asked to find the value of the expression xy²z.

First: Calculate y²

• y = 2i
• y² = (2i)² = 4i² = 4(-1) = -4 (since i² = -1)

Second: Multiply x by y²

• x·y² = (3i)·(-4) = -12i

Finally: Multiply the result by z

• xy²·z = (-12i)·(m+i)
• xy²z = -12im - 12i²
• xy²z = -12im + 12 (again, because i² = -1)

The final expression for xy²z is -12im + 12.