Euler's Formula

**Joanie** · April 21st 2009, 09:42 AM

Use Euler's Formula to write 2sq.rt.2 -2isq.rt.2 in exponential form.

My answer: 4e^i(7pi/4)

I just need confirmation that my answer is correct. Thanks.

**Rapha** · April 21st 2009, 09:53 AM

Originally Posted by Joanie

Use Euler's Formula to write 2sq.rt.2 -2isq.rt.2 in exponential form.

My answer: 4e^i(7pi/4)

I just need confirmation that my answer is correct. Thanks.

$2\sqrt{2}-2i \sqrt{2} \not= 4e^{i*(7pi/4)}$

**Joanie** · April 21st 2009, 10:40 AM

I redid the problem: Use Euler's formula to write 2sqrt(2)-2isqrt(2) in exponential form.

I was told by this forum that my answer 4e^i(7pi/4) is incorrect.

Is 4e^i(pi/4) the correct answer? If not, where am I making the error?

Thanks.

**Rapha** · April 21st 2009, 09:50 PM

Originally Posted by Joanie

I redid the problem: Use Euler's formula to write 2sqrt(2)-2isqrt(2) in exponential form.

I was told by this forum that my answer 4e^i(7pi/4) is incorrect.

Is 4e^i(pi/4) the correct answer? If not, where am I making the error?

No, this is wrong, too.

It is

$a+ib = r*e^{i*\phi},$

where $r^2 = a^2+b^2$

in this case: $r^2 = (2\sqrt{2})^2+ (2\sqrt{2})^2= 4*2+4*2 = 16$

=> $r = 4$

and $\phi = -arccos(a/r)$ (because a > 0, b <0)

in this case $\phi = -arccos(1) = -pi/4$

=> $2\sqrt{2}-2i \sqrt{2} = 4e^{i*(-pi/4)} = 4cos(- pi/4) + 4sin(-pi/4)i$

Yours,
Rapha

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