Thursday, 25 August 2016

algebra precalculus - How to calculate sqrtfrac34i











I know that the answer to 34i is 12i. But how do I calculate it mathematically if I don't have access to a calculator?


Answer



One of the standard strategies (the other strategy is to do what JM suggested in the comment to the qn) is to complete the square and use the fact that i2=1.



34i




Add and subtract 1 to get:



34+1i1



Use i2=1 to get:



34+1i+i2



Simplify 34+1 to get:




14i+i2



Rewrite i as 212i to get:



122212i+i2



Complete the square to get:



(12i)2




Get rid of the square root to get:



12i


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