Complex numbers

[Violagirl]

Hi I'm not sure what I'm doing wrong on two problems.

1. Plot the complex number in the complex plane and write it in polar form. Express the argument in degrees.

-3i

When I did tan theta, I know it's supposed to be set up as -3/0 but I don't understand how it's possible since normally it would be undefined right?

2. Write the complex number in rectangular form.

4(cos 7pi/4+i sin 7pi/4)

For an answer I got 2 sq.rt. of 2+ 2 square root of 2. But in my book it says it supposed to be subracted instead of added. Why is that?

Thanks!

 

[DrMike]

1. Plot the complex number in the complex plane and write it in polar form. Express the argument in degrees.

-3i

When I did tan theta, I know it's supposed to be set up as -3/0 but I don't understand how it's possible since normally it would be undefined right?

Technically, for a+bi, you shouldn't be solving tan(theta)=b/a, rather, r.cos(theta)=a and r.sin(theta)=b.

As you've noticed, tan(theta)=b/a lets you down when a=0. However, "r.cos(theta)=a and r.sin(theta)=b" gives cos(theta)=0, r.sin(theta)=-3. Can you work it out from here?

2. Write the complex number in rectangular form.

4(cos 7pi/4+i sin 7pi/4)

For an answer I got 2 sq.rt. of 2+ 2 square root of 2. But in my book it says it supposed to be subracted instead of added. Why is that?

I'd suggest you check carefully your work. Especially, what did you write for sin(7pi/4) ? (I get -1/sqrt(2))

Thanks![/quote]

 

[fasteddie65]

1. Plot the complex number in the complex plane and write it in polar form. Express the argument in degrees.

-3i

When I did tan theta, I know it's supposed to be set up as -3/0 but I don't understand how it's possible since normally it would be undefined right?

You might plot the number -3i in the complex number plane as (0, -3). Notice that it is on the y-axis, 3 units below the origin, or pole.

Clearly r = 3, and I think you realize that the angle is -90° or 270°.

So -3i = 0 - 3i = (3, 270°).