# How To Evaluate Complex Numbers

• urduworld
In summary: ithey are multiplying by 3-4i, so by the fifth multiplication, the result will be 9+ 16+ 24i, or 35i.
urduworld
Hi PFs

i want to know how to evaluate the complex number, and what are the meaning of the evaluating a complex number

Let Z be the complex number, Z = (3-4i)^5 what i have to do, just give me hint

urduworld said:
Hi PFs

i want to know how to evaluate the complex number, and what are the meaning of the evaluating a complex number

Let Z be the complex number, Z = (3-4i)^5 what i have to do, just give me hint

Put the complex number into its polar representation: r.e.

its polar representation is Z = r[Cos(thita) + iSin(thita)]
is it is Evaluation
i want to know what actually i have to do in evaluation

urduworld said:
its polar representation is Z = r[Cos(thita) + iSin(thita)]
is it is Evaluation
i want to know what actually i have to do in evaluation

You need to go in the reverse direction, using x and y as your variables, not r and θ. Can you complete the following with substitutions for r and θ in terms of x and y?

$$r^{i\theta} = x + iy$$​

Alternatively, can you rewrite 3-4i into polar form, to, say, four decimal places?

Cheers -- sylas

i was thinking that evaluation is like polar form i don't know how to resolve this, i know nothing about
$$r^{i\theta} = x + iy$$
please tell me what i have to do,

To find powers you need "DeMoivre's formula":
$$(r[cos(\theta)+ i sin(\theta)])^n= r^n (cos(n\theta)+ i sin(n\theta))$$.

If DeMoivre's formula is not in your text, did you consider just sitting down and multiplying 3- 4i by itself 5 times? That would probably have been faster.

oOps this is like that yes Demorvies theorem is in mine book, i have to apply this, and is n will the power like 0,1,2...n

urduworld said:
i was thinking that evaluation is like polar form i don't know how to resolve this, i know nothing about
$$r^{i\theta} = x + iy$$
please tell me what i have to do,

I fool so feelish...

HallsofIvy is quite right; simply multiplying it is probably the easiest thing to do when you have an integer exponent.

For example:
$$(3-4i)(3-4i) = 9 - 24i + 16i^2 = 9 - 16 - 24i = -7 -24i$$​
Keep going from there. Multiply by (3-4i), and again, and once more. You don't need the polar form.

However, since I mentioned it, I'd better go ahead with the answer:
$$\sqrt{x^2+y^2} \times e^{\text{atan2}(y, x) i} = x + iy$$​

Cheers -- sylas

## What are complex numbers?

Complex numbers are numbers that consist of 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 square root of -1.

## How do you evaluate complex numbers?

To evaluate a complex number, you need to combine the real and imaginary parts. This can be done by adding or subtracting the real parts and the imaginary parts separately. For example, to evaluate 3 + 2i, you would add 3 and 2i to get 5 + 2i.

## What is the difference between a real number and a complex number?

A real number is a number that can be expressed on a number line and does not have an imaginary part. A complex number, on the other hand, has both a real and an imaginary part.

## How do you simplify complex numbers?

To simplify a complex number, you need to combine like terms. This means adding or subtracting the real parts and the imaginary parts separately. For example, to simplify 3 + 2i + 5 - 4i, you would combine 3 and 5 to get 8, and combine 2i and -4i to get -2i. This simplifies to 8 - 2i.

## What are some applications of complex numbers?

Complex numbers have many applications in mathematics, physics, and engineering. They are used to represent and solve problems involving AC circuits, differential equations, and signal processing. They are also used in quantum mechanics and electromagnetism.

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