# Solving Complex Number Problems: z1 & z2

• Lmck33
In summary, complex numbers are numbers that have both a real and an imaginary part, represented as a + bi. To add or subtract complex numbers, combine the real and imaginary parts separately. To multiply, use the FOIL method. To divide, multiply by the complex conjugate of the denominator. Complex numbers have practical applications in fields such as engineering, physics, and finance.
Lmck33

## Homework Statement

Let z1 = 4 + 3i and z2 = 2 - 5i. Find each of the following in the form
x + iy, showing the details of your work:

I'll show in the photo the 2 questions i require help with.

Complex numbers

## The Attempt at a Solution

attempted f) 1/z^2 = z1 = 4+3i

z1 = 4/25 - 3i/25

However I'm really lost, mind blank and more so with question e) :S

Thanks for any help .

#### Attachments

• 1.jpg
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z*zbar=|z|^2.

Part e is just some real number.

Write down the expression and do the multiplication.

## 1. What are complex numbers?

Complex numbers are numbers that contain both a real and an imaginary part. They are represented 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. How do I add or subtract complex numbers?

To add or subtract complex numbers, simply combine the real parts and the imaginary parts separately. For example, (3 + 2i) + (1 + 4i) = (3 + 1) + (2 + 4)i = 4 + 6i.

## 3. How do I multiply complex numbers?

To multiply complex numbers, use the FOIL method. For example, (3 + 2i)(1 + 4i) = 3 + 12i + 2i + 8i^2 = 3 + 14i - 8 = -5 + 14i.

## 4. How do I divide complex numbers?

To divide complex numbers, multiply both the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of a + bi is a - bi. For example, (3 + 2i) / (1 + 4i) = (3 + 2i)(1 - 4i) / (1 + 4i)(1 - 4i) = (3 + 12i - 2i - 8i^2) / (1 + 16) = (11 + 10i) / 17.

## 5. How can I use complex numbers to solve real-world problems?

Complex numbers can be used to represent and solve real-world problems involving alternating currents, electrical circuits, and signal processing. They can also be used in engineering, physics, and other sciences to model and analyze complex systems. In addition, complex numbers have applications in finance, economics, and statistics.

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