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Express 6i in the form re^(i theta).

I have the steps. My book says 6i = r cos theta + ir sin theta
Then r=6. How?

I understand why we use Euler's formula.

|dw:1440264204510:dw|

That is what @phi and @IrishBoy123 said, too, but I still need to understand the actual math.

Like, I see and think I get the graph. My book has it.

thus if you start with
0 + 6 i
and find the magnitude, you will get 6
that means r = 6

How did you get the 0 in 0+6i?

6i is 0 + 6i (if we insist on showing the real component is 0)

Oh. The z=x+iy formula. Ok.

So now I need tan-1, which is 6/0?

yes, the angle can be found using inverse tan imag/real

Thanks! So to express it in that certain form, It must be 6e^(i pi/2)

yes, you are using Euler's
\[ e^{ix}= \cos x + i \sin x \]

|dw:1440264786581:dw|

Why does my calc say tan 6/0 is undef and yall get pi/2?

because 6/0 is undefined

ask it for \(arctan \frac{6}{0.00000001}\)

got 1.57

ok tks

Can yall help me with one more? 4-sqrt(2)i?

Do I need to multiply it by 4+sqrt(2)i?

you can do sum of squares (then take the square root)

Ok. Let me get that ans for ya!

Its just 16+2 right?

yes
if you plot it, you see it's pythagoras

Why does the book say sqrt(16+2) and then 3 sqrt(2)?

|dw:1440265488511:dw|

If I took a picture of the book, would you help me make sense of what its saying?

do you get that the length (distance from the origin) of the point 4 + sqr(2) I
is sqr(18)?

Yes. But this book does not do it that way.

It starts under the 6i

oh you take sqrt to get mag.

Yea, I see where pythagoras helps understand that now.

Thanks for that.

this is from the Gospel of St Mary [Boas, Maths for Physical Sciences]
notice how the Argand diagram features prominently

Wow that is really nice to have. Thanks!

Just solved 3 on my own got em all right

https://gyazo.com/a85e151f5d058e0a0a631873c5c59849

you have 30 seconds!