Question

simplify.
-2i(-9i)
write your answer in the form a + bi.

Explanation:

Step1: Multiply the coefficients and the imaginary units

We know that \(i^2 = - 1\). First, multiply \(-2i\) and \(-9i\). When multiplying two complex numbers in the form of \(ai\) and \(bi\) (where \(a=-2\) and \(b = - 9\) here), we use the rule \((ai)\times(bi)=abi^{2}\). So \((-2i)\times(-9i)=(-2)\times(-9)\times i\times i = 18i^{2}\)

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

Since \(i^{2}=-1\), we substitute this value into the expression \(18i^{2}\). So \(18i^{2}=18\times(- 1)=- 18\)
And we can write \(-18\) in the form \(a + bi\) as \(-18+0i\)

Answer:

\(-18 + 0i\)