Question

1. consider the complex number $i\sqrt{10}$. 4a what is the real coefficient? real coefficient = 0 4b what is the imaginary coefficient? imaginary coefficient = $\sqrt{10}$ 4c identify the type(s) of number this is. nonreal complex a pure imaginary b real c

Explanation:

Step1: Recall complex - number form

A complex number is in the form $z=a + bi$, where $a$ is the real part and $b$ is the imaginary part. For the complex number $z = i\sqrt{10}=0 + i\sqrt{10}$.

Step2: Analyze non - real complex

A non - real complex number has a non - zero imaginary part. Here, $a = 0$ and $b=\sqrt{10}
eq0$, so it is non - real complex.

Step3: Analyze pure imaginary

A pure imaginary number has a real part equal to 0. Since the real part $a = 0$ for $z = i\sqrt{10}$, it is pure imaginary.

Step4: Analyze real number

A real number has an imaginary part equal to 0. Since the imaginary part $b=\sqrt{10}
eq0$, it is not a real number.

Answer:

A. nonreal complex
B. pure imaginary