Question

question image
3+2i \t5 \t4i \t-3i \t\frac{4}{3} \t\sqrt{5}
real \ta \tb \tc \td \te \tf
imaginary \tg \th \ti \tj \tk \tl
complex \tm \tn \to \tp \tq \tr
q. which numbers are complex? select all that apply

Explanation:

Step1: Define complex numbers

A complex number is defined as $a+bi$, where $a,b\in\mathbb{R}$ (real numbers), and $i^2=-1$.

Step2: Classify each number

• $3+2i$: $a=3, b=2$ → complex.
• $5$: $a=5, b=0$ → complex (real subset).
• $4i$: $a=0, b=4$ → complex (imaginary subset).
• $-3i$: $a=0, b=-3$ → complex (imaginary subset).
• $\frac{4}{3}$: $a=\frac{4}{3}, b=0$ → complex (real subset).
• $\sqrt{5}$: $a=\sqrt{5}, b=0$ → complex (real subset).

Answer:

M. $3+2i$, N. $5$, O. $4i$, P. $-3i$, Q. $\frac{4}{3}$, R. $\sqrt{5}$