3i(1-i) ?

Options

A. 3+3i
B. 3-3i
C. 6i
D. 6

Answer

To solve the expression \( 3i(1 - i) \), we will follow these steps:

### Step 1: Distribute \( 3i \) into the expression \( (1 - i) \)
We start by applying the distributive property:
\[ 3i(1 - i) = 3i \cdot 1 - 3i \cdot i \]
This simplifies to:
\[ 3i - 3i^2 \]

### Step 2: Substitute the value of \( i^2 \)
We know that \( i^2 = -1 \). Therefore, we can substitute \( i^2 \) in our expression:
\[ 3i - 3(-1) \]

### Step 3: Simplify the expression
Now, we simplify the expression:
\[ 3i + 3 \]

### Step 4: Rearrange the expression
We can rearrange the expression to present it in standard form:
\[ 3 + 3i \]

Thus, the final result of the expression \( 3i(1 - i) \) is:
\[ \boxed{3 + 3i} \]

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