Question

1. write $-\sqrt{-49}$ as an imaginary number using $i$.

type the answer in the box below.

1. write $(5i)^2$ as either an integer or an integer multiple of $i$.

type the answer in the box below.

1. describe where to find the complex number $2 - 6i$ on the complex plane.

Explanation:

Step1: Rewrite sqrt(-49) using i

$\sqrt{-49} = \sqrt{49 \times (-1)} = 7i$, so $-\sqrt{-49} = -7i$

Step2: Expand and simplify (5i)^2

$(5i)^2 = 5^2 \times i^2 = 25 \times (-1) = -25$

Step3: Locate 2-6i on complex plane

A complex number $a+bi$ maps to $(a,b)$ on the complex plane, where $a$ is the real (x-axis) coordinate and $b$ is the imaginary (y-axis) coordinate.

Answer:

1. $-7i$
2. $-25$
3. Plot the point with x-coordinate 2 (real part) and y-coordinate -6 (imaginary part) on the complex plane, or state: "It is the point (2, -6) where the horizontal axis is the real axis and the vertical axis is the imaginary axis."