How do you simplify #sqrt(-4) - sqrt(-25)#?

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Answer 1 · 2018-08-03T19:45:07

#z=-3i orz=3i#

We know for the complex numbers : #i^2=-1#

Let ,

#z=sqrt(-4)-sqrt(-25)#

#=>z=sqrt(4(-1))-sqrt(25(-1))#

#=>z=sqrt(4i^2)-sqrt(25i^2)#

#=>z=sqrt((2i)^2)-sqrt((5i^2))#

#=>z=(+-2i)-(+-5i)#

#=>z=(2i)-(5i) or z=(-2i)-(-5i)#

#=>z=-3i orz=3i#

Answer 2 · 2018-08-03T23:03:41

#pm3i#

Recall that #sqrt(-1)=i#. With this in mind, we can rewrite this as

#sqrt4sqrt(-1)-(sqrt(25)sqrt(-1))#

#=>+-2i-(+-5i)#

#=>2i-5i=-3i# and #-2i-(-5i)=5i-2-=3i#

Therefore, our solutions are #pm3i#.

Hope this helps!