Daily Math · 2026-06-06

Question 1

The value of $(1 + i)^2$ is:

Accepted Answer

$(1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i$.

Answer

$1$

Answer

$1 + 2i$

Answer

$2i$

Answer

$1 - 2i$

Question 2

If the mean of $\{x_1, x_2, \ldots, x_n\}$ is $\bar{x}$, the mean of $\{x_1 + 5, x_2 + 5, \ldots, x_n + 5\}$ is:

Accepted Answer

$\dfrac{1}{n}\sum (x_i + 5) = \dfrac{1}{n}\sum x_i + 5 = \bar{x} + 5$.

Answer

$\bar{x}$

Answer

$\bar{x} + 5$

Answer

$5\bar{x}$

Answer

$\bar{x} + \dfrac{5}{n}$

Question 3

The equation $\cos x = x$ has at least one solution in:

Accepted Answer

$g(0) = 1 > 0$, $g(\pi/2) = 0 - \pi/2 < 0$. Since $g$ is continuous, by the IVT there is $c \in (0, \pi/2)$ with $g(c) = 0$, i.e. $\cos c = c$.

Answer

$(-1, 0)$

Answer

$(0, \pi/2)$

Answer

$(\pi, 2\pi)$

Answer

nowhere

Problems & worked solutions