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Pre-Calc Problem. Please Help?
Hey so i have about 4 pre-calc problems i really need help for.
1. Write the expression in the form a + bi
5 + i / 5 - i
2. Show that (√2 / 2 ) (1 + i) is a square root of i.
3. Find the values of the function f(x)= x^3 - 9x. (Remember i= √-1) Provide each answer in simplest exact form.
a) f ( -√2/3)
b) f (i√3)
c) f ( x / 3)
d) f (x-3)
It would help if the explanation of how u got to the answer was included. Thanks ya'll
1 Answer
- ?Lv 49 years agoFavorite Answer
1). You have to rationalize the denominator,which means you multiply by (5+i) and divide by (5+i)
[(5+i)/(5-i)]×[(5+i)/(5+i)]=[(25+10i +i^2)/(25+1)]
=(24+10i)/26 = 12/13 + 5/13 i
2)Raise (√2 / 2 ) (1 + i) to 2 and it becomes
(√2 / 2 )^2 (1 + i)^2=(2/4)(1+2i+i^2)=1/2(1+2i-1)=1/2 × 2i=i
3)a.f ( -√2/3)=( -√2/3)^3 -9( -√2/3)
=(-2√2/9)+9√2/3=(-2√2/9)+3√2=25√2/9
b) f (i√3)=(i√3)^3-9(i√3)=-3√3i -9√3i=-12√3i
c)f ( x / 3)=( x / 3)^3 - 9(x/3)=x^3/9 -3x=(x^3-27x)/9
d)f (x-3)=(x-3)^3 - 9(x-3)=x^3-9x^2+27x-27-9x+27
=x^3-9x^2+18x
