Expert: Sherry Wallin - 10/29/2009

Question
Can you help me solve the following questions?
21. y²+400 = 0
22. 4z² + 39 = 7
23.(4 + i)(4 - i)
35.(2 - 3i)2(2 + 3i)2

Answer
Hi Krystal~
    Let me clarify something for you first. The word 'solve' means to find a value for a variable in an equation. 21 and 22 are equations but 23 and 24 are not. How do you know if you have an equation? That is simple, were you given an equal sign, were you told to find the value of the variable? To sum this up, when there isn't an equal sign you cannot talk about solving, there is no solving, only simplification and usually that means making what you start with simpler by reducing it or combining like terms etc. I hope this clears that part up for you.   
   Secondly, I will talk you through what you should be doing and thinking for each of your problems but will not necessarily give you the answers.

21 You cannot find a real number so that when you square it it is negative. here Y^2+ 400 = 0 implies that y^2 = -400. Can you find a 'real' number so that when you square it you get a negative number? The answer is no, there is no real number, there is however an imaginary number. Use what I gave you y^2 = -400 to find the imaginary solutions. I am assuming by the 4 problems you gave me that you are allowed to find complex solutions.

22  Since there is no middle term move all the constants together, this means move the 39 to the right which will give you -32 on the right hand side. Now you have 4z^2 = -32, divide by 4 giving you z^2 = -8, take the square root of both sides and I will leave the rest up to you to find.

23 Use foil, combine our inner and outer terms to make a middle term (if there is one, in this case there won't be). Keep in mind every time you get a factor of i^2 it is replaced by -1.

24 You have 4 factors here and two of them are real, put them together 2*2 =4 so you really have
4(2 - 3i)(2 + 3i)=4[(2 - 3i)(2 + 3i)] multiply what is inside of the [ ] (hint use foil and replace all i^2 with -1)and simplify and then multiply that answer by 4

I hope this helps you.

Math Prof