The task asks to "Plot points corresponding to complex numbers" for Variant 6, where three complex numbers are provided:

1. $z_1 = -6$
2. $z_2 = 2 + i$
3. $z_3 = -3 - 3i$

To solve this problem, we need to understand that a complex number $z = a + bi$ can be represented as a point in the complex plane (often called the Argand plane), where:

• The real part $a$ is plotted along the horizontal (real) axis.
• The imaginary part $b$ is plotted along the vertical (imaginary) axis.

Steps:

1. Plot $z_1 = -6$:

   • This is a purely real number, where the imaginary part is 0.
   • So, plot this point on the real axis at $(-6, 0)$, which is 6 units to the left of the origin on the horizontal axis.

2. Plot $z_2 = 2 + i$:

   • Here, the real part is 2, and the imaginary part is 1.
   • The point will be $(2, 1)$, which means move 2 units right on the real axis and 1 unit up on the imaginary axis.

3. Plot $z_3 = -3 - 3i$:

   • The real part is -3, and the imaginary part is -3.
   • The point will be $(-3, -3)$, which is 3 units left on the real axis and 3 units down on the imaginary axis.

Explanation:

• Each complex number corresponds to a point on the complex plane based on its real and imaginary components.
• $z_1$ is located purely on the real axis, while $z_2$ and $z_3$ have both real and imaginary components, placing them in the first and third quadrants, respectively.

Would you like more details on the plotting process or any further explanation on complex numbers?

Here are 5 related questions to extend the learning:

1. How do you convert a complex number from rectangular form to polar form?
2. What is the geometric significance of multiplying two complex numbers?
3. How can we calculate the magnitude (or modulus) of a complex number?
4. What are the applications of complex numbers in electrical engineering?
5. How can you visualize the addition of two complex numbers on the Argand plane?

Tip: When working with complex numbers, always remember that the real part corresponds to horizontal movement, while the imaginary part corresponds to vertical movement in the complex plane.