Questions: Perform the operation and write the result in standard form. 14 i(1-7 i)

Transcript text: Perform the operation and write the result in standard form. \[ 14 i(1-7 i) \]

Solution

Solution Steps

To solve the given problem, we need to perform the multiplication of the complex number \(14i\) with the complex number \((1 - 7i)\). We will use the distributive property to expand the expression and then simplify it to standard form \(a + bi\).

Step 1: Define the Complex Numbers

We start with the complex numbers \(14i\) and \(1 - 7i\).

Step 2: Perform the Multiplication

We use the distributive property to multiply the complex numbers: \[ 14i \cdot (1 - 7i) \]

Step 3: Expand the Expression

Expanding the expression, we get: \[ 14i \cdot 1 + 14i \cdot (-7i) = 14i - 98i^2 \]

Step 4: Simplify Using \(i^2 = -1\)

Since \(i^2 = -1\), we can simplify the expression: \[ 14i - 98(-1) = 14i + 98 \]

Step 5: Write the Result in Standard Form

The result in standard form \(a + bi\) is: \[ 98 + 14i \]

Final Answer

\(\boxed{98 + 14i}\)

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