Solve 3-7i/2+3i: Imaginary Numbers

• Echo 6 Sierra
In summary, the conversation revolved around explaining how to work the equation 3-7i/2+3i, with the main suggestion being to multiply both the numerator and denominator by the complex conjugate of the denominator. Another suggestion was to change the equation to polar form and divide the radii while subtracting the angles. The conversation also touched on the importance of including parenthesis in the equation, and apologies were made for any mistakes.

Echo 6 Sierra

Could someone PULEEZ explain how to work the following equation:

3-7i/2+3i

For the life of me I cannot sqeeze this into my brain!

Have you tried multiplying both the Numerator and Denominator by the complex conjugant of the Denominator?
…Don’t forget to use the FOIL method.

Huh? That doesn't look like a multiplication problem to me, Boulder.

Echo, when adding and subtracting complex terms (imaginary and real), you just keep the like terms together.

In other words, you add the imaginary parts, and then you add the real parts.

For example:

3+8+5i+7i/4=

(3+8)+(5+7/4)i=

11+(27/4)i

We had conversed through PM and Echo 6 Sierra didn't make me aware of this. We treated the problem as;

(3-7i)/(2+3i)

Perhaps Echo 6 Sierra can clarify, as I assumed the parenthesis had been mistakenly omitted. If not, my mistake then.

Last edited by a moderator:
Ah hah.

Gotcha. Parenthesis. Yes, that would be division then, wouldn't it?

Yes, I apologize. I mistakenly omitted them. Also, another apology is in order. I mistakenly posted here instead of the Homework section. Thank you both for your input.

Hm...Did you solve it yet?

But yea, conjugate of the denomitator is how u do it...

OR

You can change it to polar ( i think that's what its called) And then u have
r*cis([0])
r2*cis([0]2)
and u just divide the radii and subtract the angles...Not sure tho..i know for multiplication u multiply the radii and add the angles so i would assume u do the opposite for division

Problem solved. Thank you to everyone for your input.

1. What is an imaginary number?

An imaginary number is a number that cannot be expressed as a real number. It is represented by the letter i and is defined as the square root of -1. Imaginary numbers are useful in solving problems that involve negative numbers and are commonly used in complex numbers.

2. How do you simplify the expression 3-7i/2+3i?

To simplify the expression 3-7i/2+3i, we first need to combine like terms. In this case, we have two imaginary numbers -7i and 3i. When adding or subtracting imaginary numbers, we can treat i as a variable and combine the real and imaginary parts separately. So, 3-7i/2+3i can be rewritten as 3+(3-7)/2i. This simplifies to 3-2i.

3. Can you graph imaginary numbers?

Yes, imaginary numbers can be graphed on the complex plane. The x-axis represents the real part of the number, while the y-axis represents the imaginary part. For example, the imaginary number 3i would be graphed at the point (0,3) on the complex plane. However, it's important to note that imaginary numbers cannot be graphed on a traditional number line since they do not fall on a single line.

4. How are imaginary numbers used in real life?

Imaginary numbers are used in various fields of science and mathematics, including electrical engineering, quantum mechanics, and signal processing. In electrical engineering, they are used to represent the current and voltage in alternating current circuits. In quantum mechanics, they are used to describe the wave function of particles. In signal processing, they are used to filter out noise from signals.

5. How do you solve equations with imaginary numbers?

To solve equations with imaginary numbers, we use the same algebraic rules as we do for real numbers. However, we need to remember that the square root of -1 is i, and we can also perform operations on the imaginary part of the number. For example, to solve the equation 2x + 3i = 0, we would first subtract 3i from both sides to get 2x = -3i. Then, we divide both sides by 2 to get x = -3i/2.