Question 1206982
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I'm having trouble with the following example problem:
Find the square roots of the complex number. (Enter your answers as a comma-separated list.)
−10i
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<pre>
Apply deMoivre formula. The square root of -10i has two different values.

Their modulus is {{{sqrt(10)}}}.  Their arguments are  {{{3pi/4}}}  and {{{3pi/4+pi}}} = {{{7pi/4}}}.


So, one value of the square root is  {{{sqrt(10)*(cos(3pi/4) + i*sin(3pi/4))}}} = {{{sqrt(10)*(-sqrt(2)/2 + i*(sqrt(2)/2)))}}} = {{{-sqrt(20)/2 + i*(sqrt(20)/2))}}}.


The other value of the square root is  {{{sqrt(10)*(cos(7pi/4) + i*sin(7pi/4))}}} = {{{sqrt(10)*(sqrt(2)/2 - i*(sqrt(2)/2)))}}} = {{{sqrt(20)/2 - i*(sqrt(20)/2))}}}.


<U>ANSWER</U>.  Two values of the square root of -10i are  {{{-sqrt(20)/2 + i*(sqrt(20)/2))}}}  and  {{{sqrt(20)/2 - i*(sqrt(20)/2))}}}.
</pre>

Solved.


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On deMoivre formula see your textbook or the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/How-to-take-a-root-of-a-complex-number.lesson>How to take a root of a complex number</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/Solved-problems-on-de%27Moivre-formula.lesson>Solved problems on de'Moivre formula</A>

in this site.


Other relevant lessons in this site, related to square roots of complex numbers are

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/How-to-take-a-square-root-of-a-complex-number.lesson>How to take a square root of a complex number</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/Solved-problem-on-taking-square-roots-of-complex-numbers.lesson>Solved problem on taking square root of complex number</A>

Learn the subject from there.



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What @MathLover1 wrote in her post, is irrelevant to the solution of the problem.

For safety of your mind, simply ignore her post.