Math Help - Complex Numbers Help!

1. Complex Numbers Help!

How do I find the argument for a value such as:

(-2(square root3) + 6i)/(2i)

This kind of example confuses me. Do you divide the 6i by 2i to simplify?

2. Multiply the equation by 2i/2i and then simplify.
The denominator will become -4.
The final answer is 3+sqrt(3)i. The in between you should do.

3. $\frac{{ - 2\sqrt 3 + 6i}}{{2i}}\left( {\frac{{ - 2i}}{{ - 2i}}} \right) = \frac{{12 + 4\sqrt 3 i}}{4} = 3 + \sqrt 3 i
$

4. Oh yes, -2i being the complex conjugate. Thanks.

5. Euler's Formula

In the attached question, the second pair of brackets. Using the formuala I get:

((1/sqrt3) * (sqrt3/2)) - ((1/sqrt3) * (1/2))

Edit: I think I got it using the second bracket as i, and multiplying by the first set of brackets in the question. Is the answer D?

6. the answer is actually A. i cant write the Latex too well though to give steps

7. Okay, I see where I went wrong. Got a wrong sign.

8. How do I do this example. I've tried Eular's Forumla on the bottom line but I can't get to the correct answer.

9. Originally Posted by haku
How do I do this example. I've tried Eular's Forumla on the bottom line but I can't get to the correct answer.

you should be working writing the numerator as $ae^{i \theta}$

10. Okay, doing that gives me:

(-e^(i2Pi/3)) / (4e^(iPi/3))

How do I solve from here?

11. Originally Posted by haku
Okay, doing that gives me:

(-e^(i2Pi/3)) / (4e^(iPi/3))

How do I solve from here?
you made a mistake, try finding the mod and arg again

12. Okay, the modulus is 2, and the arg is 120 because it's in the second quadrant. So:

((-2e^(i2Pi/3))/(4e^(iPi/3))

Is that correct?

13. Originally Posted by haku
Okay, the modulus is 2, and the arg is 120 because it's in the second quadrant. So:

((-2e^(i2Pi/3))/(4e^(iPi/3))

Is that correct?
i got the numerator as $2e^{i \frac{2 \pi}{3}}$

14. Yes, 120 degrees. That's what I attempted to type in. How does it simplify from then on? Do you subtract the imaginary numbers to give answer D?

15. yes the answer is D.

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