# Solving Complex Number Problems: Rectangular and Polar Form

• Ben_sa
In summary, the conversation is about a problem with solving a complex number equation. The user asks for help with finding the value in both rectangular and polar form. The final answer should be 3.769 + j1.538.
Ben_sa
Hello all
I am having this problem with complex number and i don't know exactly how to solve it. Can i get some help with it please:

i) Z1 = 2 + j5, Z2 = 1 – j3 and Z3 = 4 – j determine, in both rectangular and polar form, value of
((Z1 * Z2)/(Z1 + Z2)) + Z3
(Give the final answers to 3 significant figures).

Thanx

Welcome to the forums Ben,

Just for future reference there are homework forums, specifically for homework questions. In addition, the rules of the forums state that one must show ones attempt at a question before receiving help...

Sorry i forgot about that in the rules
this is my work that i did i hope it is right

((2+j5) * (1-j3))/((2+j5) + (1-j3))

= 2 - j3 +j5 +15/(3+j2)

=((17+2J) * (3-j2))/((3+j2) * (3-j2))

=55 +42j/13

= (4.231 + 3.231j) + (4-j)
= (8.231 + 2.231j)

is that right??
Next time I'll remember to put it in the homework section

The previous answer i think was wrong and i think this one is the right one
= 3.769 + j1.538
because there was a mistake in the second line

Ben_sa said:
((2+j5) * (1-j3))/((2+j5) + (1-j3))
This line, however, is correct. Just check your arithmetic.

## 1. What are complex numbers?

Complex numbers are numbers that contain both a real part and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part, with i being the imaginary unit (√-1).

## 2. What is the problem with complex numbers?

The main problem with complex numbers is that they are often difficult to visualize and understand, as they do not fit on a traditional number line. Additionally, some calculations involving complex numbers can be complex and time-consuming.

## 3. How are complex numbers used in science?

Complex numbers are used in a variety of scientific fields, including physics, engineering, and mathematics. They are often used to represent quantities with both magnitude and direction, such as electrical currents and electromagnetic fields.

## 4. Can complex numbers have real-world applications?

Yes, complex numbers have many real-world applications. They are used in signal processing, control systems, and even in the design of computer graphics and animations.

## 5. Are there any limitations to using complex numbers?

One limitation of using complex numbers is that they cannot be used in certain physical situations, such as representing physical quantities that are always positive (e.g. mass, energy). Additionally, some calculations with complex numbers can result in non-real solutions, which may not have a physical meaning in certain contexts.

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