# Tricky complex numbers problem

• andrew.c
In summary, the problem asks to find the new position of z2, a point in the complex plane, after being rotated 450 degrees around z1, another point in the complex plane. To solve this, find the difference between z2 and z1, rotate it by pi/4 radians, and add the result back to z1.
andrew.c

## Homework Statement

z1 = 1 + i, z2 = i − 5 are points in the complex plane. If z2 is rotated about z1 by 450
find its new position.

Attempt at solution
Absolutely no idea! I think I might need to use e^theta*i but not sure!

What does that mean rotated about z1 by 450? Could you elaborate?

Sorry, that's all that was given...
I think it means like rotating 45 degs through the imaginary axis?

But then what does that have to do with Z1.

45 degrees is pi/4 radians. To rotate around another point, find the difference z2-z1 and rotate that by pi/4 (sure, multiply by e^(i*pi/4)). Add the result back to z1.

thank you!

## 1. What are complex numbers?

Complex numbers are numbers that include both a real part and an imaginary part. They are typically written in the form a + bi, where a is the real part and bi is the imaginary part, with i representing the square root of -1.

## 2. What makes the complex numbers problem tricky?

The complex numbers problem can be tricky because it involves working with both real and imaginary numbers, which can be difficult to visualize and manipulate. It also requires a good understanding of complex number operations and properties.

## 3. How do you solve a tricky complex numbers problem?

To solve a tricky complex numbers problem, you first need to identify the given numbers and operations involved. Then, use the properties of complex numbers to simplify the problem and find the solution. It may also be helpful to graph the complex numbers on a complex plane to visualize the problem.

## 4. Can you provide an example of a tricky complex numbers problem?

One example of a tricky complex numbers problem is finding the square root of a complex number. This involves using the formula (a + bi)^1/2 = ±(a^2 - b^2)^1/2 + (2ab)^1/2i and applying it to the given complex number.

## 5. How are complex numbers used in real life?

Complex numbers are used in various fields such as engineering, physics, and economics. They are particularly useful in electrical engineering for analyzing alternating current circuits and in quantum mechanics for representing wave functions. They are also used in financial forecasting and signal processing.

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