\(5p = 10005 + 125i\\ p = \boxed{2001 + 25i}\)
\([1/2, 4/3]\)
\(i^6 + i^{16} + i^{-26} = i^4\cdot i^2 + (i^4)^4 + \frac{1}{(i^4)^6\cdot i^2} = i^2 + 1 + \frac{1}{i^2} = -1 + 1 + \frac{1}{-1} = \boxed{-1}\)
\(x^2-5x+6\ge 0 \)
\((x-2)(x-3)\ge 0 \iff x\le 2,\ x\ge 3\)
or \(\boxed{x \in (-\infty, 2] \cup [3, \infty)}\)
\((1+ 3i) + (2-4i) = \boxed{3 - i}\)
\(x^2 + bx+ 8\) = 0 has to have no real solutions. So, the discriminant neds to be less than 0.
\(\Delta = b^2 - 4ac= b^2 - 32 < 0\)
\(b^2 < 32\)
The greatest integer value of b is 5.
Understandable, have a great day.
Hint: 60 minutes make up a degree.
\(\sin(39^{\circ}20') = \sin{39 \frac{1}{3}^{\circ}}\)
and so on.
\(\text{Domain} \quad \{0, 1, \sqrt{2}, \sqrt{3}, 2, \sqrt{5}. \sqrt{6}. \sqrt{7}, \sqrt{8}, 3\}\)
This is a total of 10 values.
\(\frac{-3+4i}{1+2i} \cdot \frac{1-2i}{1-2i} = \frac{-3+4i+6i-8i^2}{5} = \boxed{\frac{11+10i}{5}}\)
