Question

simplify.
-4i + 5i
write your answer in the form a + bi.

Explanation:

Step1: Identify like terms

The expression is \(-4i + 5i\). The like terms here are the terms with the imaginary unit \(i\).

Step2: Combine like terms

To combine \(-4i\) and \(5i\), we add their coefficients. The coefficient of \(-4i\) is \(-4\) and the coefficient of \(5i\) is \(5\). So, \(-4 + 5 = 1\). Therefore, \(-4i + 5i = ( - 4 + 5)i = 1i = i\). In the form \(a + bi\), \(a = 0\) (since there is no real part) and \(b = 1\), so the expression simplifies to \(0 + 1i\) or just \(i\) (which can also be written as \(0 + i\)).

Answer:

\(0 + i\) (or simply \(i\))