# Give answer in rectangular form

• pugfug90

## Homework Statement

Find the quotient w*u, w/u, w^2
w=3(cos30 degrees + isin 30 degrees)
u=2(cos 60 degs + isin 60 degs)

## The Attempt at a Solution

I can convert polar to rectangular and back.. but trig to rectangular? Eh?

I got w*u=6i... I think that would be considered "standard form a + bi" but teacher ?typo? wrote "rectangular form"..

Rectangular form means express z in the form z=x+iy. Clearly, wu=6i is in rectangular form!

I'm researching about "rectangular form" and I'm finding it to be a+jb. But no worries, I looked up my teacher's key to the review guide, rectangular form is also a+bi or x+iy or something and who cares so case closed:)

"a and b" and "x and y" are just numbers, so there's no difference there. Some people (engineers?) take the square root of -1 to be j instead of i. They are both correct.

## 1. What is "rectangular form"?

Rectangular form is a mathematical notation used to express complex numbers in the form of a + bi, where a and b are real numbers and i is the imaginary unit.

## 2. How do you convert a complex number into rectangular form?

To convert a complex number into rectangular form, you need to separate the real and imaginary parts of the complex number and write them in the form of a + bi. For example, the complex number 3 + 4i would be written in rectangular form as 3 + 4i.

## 3. What is the purpose of using rectangular form for complex numbers?

Rectangular form allows us to easily perform mathematical operations on complex numbers, such as addition, subtraction, multiplication, and division. It also allows us to graph complex numbers on the complex plane.

## 4. Can a complex number be written in more than one rectangular form?

Yes, a complex number can be written in infinitely many rectangular forms, as long as the real and imaginary parts are the same. For example, the complex number 2 + 3i can also be written as -1 + 4i, or 5 + 1i.

## 5. Is there a way to convert a complex number from rectangular form to polar form?

Yes, there is a formula for converting a complex number from rectangular form to polar form. It involves finding the magnitude (or absolute value) of the complex number and the angle it makes with the positive real axis. The formula is z = r(cosθ + isinθ), where r is the magnitude and θ is the angle.