0
$\begingroup$

I got a problem wrong and I don't understand how. The question was to compute:

$\sqrt{-1875.5+9.68i}$

I said this would be equal to .112+43.31i because that's the number my calculator gives me. However, apparently the answer is .116+44.45i? I thought maybe it was a radians vs degrees error but even in radians my calculator does not give me .116+44.45i.

$\endgroup$
0
$\begingroup$

Your answer is perfectly correct.

What I suspect are tremedous errors because of the different sizes of the two numbers. Working with whole numbers, you want to compute $$\sqrt{-\frac{18755 }{10}+\frac{968 }{100}\,i }=\color{blue}{\frac{11}{5} \sqrt{-\frac{775}{2}+2 \,i}}$$ which is, using de Moivre, $$\frac{11 \sqrt[4]{600641}}{5 \sqrt{2}}\left(\sin \left(\frac{1}{2} \tan ^{-1}\left(\frac{4}{775}\right)\right)+i \,\cos \left(\frac{1}{2} \tan ^{-1}\left(\frac{4}{775}\right)\right) \right)$$ Any error in the evaluation of any term could have a tremendous impact on the final result.

May I ask you to compute with steps the "blue" expression and report what you get ?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.