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Chapter 2: Problem 53
Write the quotient in standard form. $$\frac{2}{4-5 i}$$
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(a) Find the interval(s) for \(b\) such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients. $$x^{2}+b x-4=0$$
Determine (if possible) the zeros of the function \(g\) when the function \(f\) has zeros at \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\) $$g(x)=3 f(x)$$
Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$h(x)=4 x^{2}-8 x+3$$
The coordinate system shown below is called the complex plane. In the complex plane, the point that corresponds to the complex number \(a+b i\) is \((a, b)\) (GRAPH CANNOT COPY) Match each complex number with its corresponding point. (i) 3 (ii) \(3 i\) (iii) \(4+2 i\) (iv) \(2-2 i\) (v) \(-3+3 i\) (vi) \(-1-4 i\)
Simplify the complex number and write it in standard form. $$(-i)^{6}$$
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