# Calculating complex numbers with my TI-84+

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.

## 1 Answer

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, $$\frac{11 \sqrt{600641}}{5 \sqrt{2}}\left(\sin \left(\frac{1}{2} \tan ^{-1}\left(\frac{4}{775}\right)\right)+i \,\cos \left(\frac{1}{2} \tan ^{-1}\left(\frac{4}{775}\right)\right) \right)$$ 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 ?