Question

multiply complex numbers (basic)
$9i \cdot (-4 - 7i) = $
your answer should be a complex number in the form $a + bi$ where $a$ and $b$ are real numbers.
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Explanation:

Step1: Distribute 9i

Using the distributive property (also known as the distributive law of multiplication over addition), we multiply \(9i\) with each term inside the parentheses. So we have \(9i\times(-4)+9i\times(-7i)\).
Mathematically, this is \(9i\cdot(-4) - 9i\cdot7i\) or \(-36i-63i^{2}\).

Step2: Recall \(i^{2}=- 1\)

We know that the imaginary unit \(i\) is defined such that \(i^{2}=-1\). Substitute \(i^{2}=-1\) into the expression \(-36i - 63i^{2}\).
So we get \(-36i-63\times(-1)\).

Step3: Simplify the expression

Simplify \(-63\times(-1)=63\). Then the expression becomes \(63 - 36i\) (we can also write it as \(63+(- 36)i\) to match the \(a + bi\) form).

Answer:

\(63-36i\)