# What is the magnitude and angle of this complex number?

• hanhao
In summary, the conversation is about finding the magnitude and angle of a complex number in terms of a and b, and converting it to the form x+iy. The person asking for help does not know how to convert it and is looking for assistance in finding the final expression. They are given a useful resource for understanding complex numbers.

#### hanhao

what is the magnitude and angle of this complex number? in terms of a and b?
http://img364.imageshack.us/img364/4262/1af2.jpg [Broken]
come i need some help

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Do you know how to convert it to the form x+iy?

neutrino said:
Do you know how to convert it to the form x+iy?
no, that's way beyond my scope
all i need is the final expression

I don't think you´ll find anyone here giving you the final expression.

You might find people willing to help you find the final expression.

You should find this useful: http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut12_complexnum.htm" [Broken].

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## 1. What is the definition of a complex number?

A complex number is a number that comprises a real number and an imaginary number. It is represented in the form a + bi, where a is the real part and bi is the imaginary part, and i is the imaginary unit equal to the square root of -1.

## 2. How do you find the magnitude of a complex number?

The magnitude (or absolute value) of a complex number is found by taking the square root of the sum of the squares of the real and imaginary parts.

For a complex number z = a + bi, the magnitude is |z| = √(a^2 + b^2).

## 3. What is the angle of a complex number?

The angle (or argument) of a complex number is the angle formed between the positive real axis and the vector representing the complex number in the complex plane.

It is measured in radians and can be found using the formula tan θ = b/a, where θ is the angle and a and b are the real and imaginary parts of the complex number, respectively.

## 4. How do you represent a complex number in polar form?

A complex number can be represented in polar form as r(cos θ + i sin θ), where r is the magnitude and θ is the angle of the complex number. This form is also known as the trigonometric form of a complex number.

## 5. Can a complex number have a negative magnitude?

No, the magnitude of a complex number is always a positive real number.

The imaginary part of a complex number may be negative, but when finding the magnitude, the negative sign is squared and becomes positive.