Question

I do not even know where to begin with this one...
Express the following complex number in trigonometric form. Round each modulus to the nearest hundredth and give each argument in radians also rounded to the nearest hundredth, positive, and in the intercal [0.2pie).

(-3+isquareroot2)/(squareroot3 +2i)^2

Answer 1

\[\frac{(-3+i \sqrt{2}) }{ (\sqrt{3}+2i)^{2} }\]

Answer 2

\[\Large
\frac{\left(\sqrt{3}+3 i\right) \left(-4 \sqrt{3}+i\right)}{\left(4 \sqrt{3}+i\right) \left(-4
\sqrt{3}+i\right)}=-\frac{1}{49} \left(-15-11 i \sqrt{3}\right)=\\
\Large
\frac{1}{49} \left(15+11 i
\sqrt{3}\right)=\frac{1}{7} \left(2 \sqrt{3}\right) e^{i \tan ^{-1}\left(\frac{11}{5
\sqrt{3}}\right)}\\\Large \text{ let }
\theta=\tan ^{-1}\left(\frac{11}{5
\sqrt{3}}\right)\\ \Large
r=\frac{1}{7} \left(2 \sqrt{3}\right)\\ \Large
Number= r ( \cos(\theta) + i\ \sin(\theta))
\]

Answer 3

so theta would be \[\frac{ 11 }{ 5\sqrt{3} }?\]

Answer 4

giving me \[\frac{ 1 }{ 7 }cis \frac{ 11 }{ 5\sqrt{3} }?\]

Answer 5

No
\[
\theta=\tan ^{-1}\left(\frac{11}{5
\sqrt{3}}\right)
\]

Answer 6

and
\[
r=\frac{1}{7} \left(2 \sqrt{3}\right)
\]

Answer 7

ok that helps a lot, thank you

Answer 8

YW