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  1. C

    Find a value of the angle from the given equation

    Homework Statement If we are given an equation that equals tg\alpha, and we need to find out how much is \alpha, how would we do it, having in mind the equation bellow? Homework Equations tg\alpha=\frac{(1+tg1)(1+tg2)-2}{(1-tg1)(1-tg2)-2} The Attempt at a Solution Since i know the answer (i...
  2. C

    Cartesian product help?I'm interested how to solve the following problem:

    I'm interested how to solve the following problem: if we have a triangle, where a,b,c are sides of that triangle and we know that (a+b+c)x(a+b-c)=3ab, we need to find the angle opposite to side c. How to do this?
  3. C

    Exponential/logarithmic equation

    Homework Statement How many numbers, where x is is a whole number, satisfy the equation. Homework Equations x*3^{log_{x}5}=15 The Attempt at a Solution Most of my attempts have been blocked due to the fact that i don't know what to do with the x that is not in the base of algorithm. I tried...
  4. C

    Finding a i b

    If a and b are real numbers, and we know that (2a-b-3)^{2} + (3a+b-7)^{2}=0, how much is 3a-7b Any ideas on this? I'm guessing the solution can go two ways: either i find a and b separately, or i calculate the expression above somehow and i'll be left with 3a-7b
  5. C

    The number of complex numbers that satisfy the equation

    Homework Statement So, i have this equation, and it is asked of me to find the number of complex numbers that satisfy the equation. (z=x+iy) Homework Equations z-\overline{z}+|z-i|=4-2i The Attempt at a Solution I tried replacing the numbers and i got something like this...
  6. C

    Question about complex numbers

    Hello guys! I have a question related to complex numbers. How would i calculate, for example (\frac{\sqrt{3}+i}{2})^{2010} without using the De Moivre's theorem?
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