🧮 algebra

1. The problem is to compute the value of the complex number $\left(-1 + \sqrt{3}i\right)^5$. 2. First, express the complex number in polar form. The complex number is $z = -1 + \s

1. Stating the problem: Simplify the expression $A=(-2)(-3)[(+4)+(-5)]\(-1)$. 2. Simplify inside the brackets: $(+4)+(-5) = 4 - 5 = -1$.

1. Énoncé du problème : Soient $a$, $m$ et $n$ trois entiers relatifs, avec $m$ et $n$ multiples de $a$. 1.a. Traduction de l'hypothèse :

1. The problem states that $P$ is proportional to $\frac{1}{2}H$, and we are given $P=2$ when $G=4$ and $H=3$. We need to find $H$ when $P=3$ and $G=8$. 2. Since $P \propto \frac{1

1. **State the problem:** We have two ascensions, Mila's and Malik's, with altitude vs time data points. We want to analyze Malik's ascension line passing through points (1, 693) a

1. **State the problem:** An intelligence officer spends 40% of his salary on rent and 20% on food. He saves 1200, which is the remaining amount after these expenses. We need to fi

1. Problem: Pronađi najmanji zajednički višekratnik (NZV) i najveći zajednički djelitelj (NZD) brojeva 48, 50 i 100. 2. Najprije ćemo pronaći NZD koristeći faktorizaciju brojeva:

1. **State the problem:** We are given three functions: $$f(x) = x^2 - 16$$

1. The problem asks to find the value of $f(5) - h(11)$. 2. To solve this, we need the definitions or expressions for the functions $f(x)$ and $h(x)$.

1. **State the problem:** We need to evaluate $f(3) + g(-3)$ given the functions: $$f(x) = x^2 - 16$$

1. **State the problem:** We are given three functions: $$f(x) = x^2 - 16$$

1. **State the problem:** We need to evaluate the function $g(x) = x^2 + x - 12$ at $x = -4$. 2. **Substitute $x = -4$ into $g(x)$:**

1. Stating the problem: Solve the equation $$\frac{3p}{12pq+4q} = \frac{8p^2}{6p^2 + 2pq}$$ and solve for $x$ in $$2x = \frac{2y^2 - 3z}{2}$$. 2. Simplify the first equation:

1. Énonçons le problème : Simplifier l'expression $$\left(\sqrt[\sqrt{b^{16d}}]{\ }\right)^{-2} \left(\sqrt[\sqrt{b^{-24d}}]{\ }\right)^{-3}$$ en utilisant les lois des exposants.

1. Énonçons le problème : Simplifier l'expression $$\left(\frac{a^4}{\sqrt{a^{10}}}\right)^4 \left(\frac{\sqrt{a^{20}}}{a^8}\right)^{-2}$$ en utilisant les lois des exposants. 2. S

1. Énonçons le problème : Simplifier l'expression $$\left( \frac{2a^{2}b^{2}}{3a^{-1}b^{2}}\right)^{-3} \left(\frac{3ab^{3}}{2a^{2}b}\right)^{-2}$$ en utilisant les lois des exposa

1. Problem: Zuordnen der grünen Terme zu den äquivalenten blauen Termen ohne Taschenrechner. 2. Vereinfachung der grünen Terme:

1. **Problem Statement:** Alia hired a taxi with a fixed charge of 1500 plus 450 per 30 minutes.

1. The problem is to simplify the expression $$16^{\frac{3}{4}}$$ and verify the equality $$16^{\frac{3}{4}} = 2^{4 \cdot \frac{3}{4}}$$. 2. Start by expressing 16 as a power of 2:

1. The problem is to find the sum of the series $$1 + i + i^2 + i^3 + i^4 + \cdots + i^{2021}$$ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. Recall the powers o

1. **Problem statement:** Solve the polynomial equation $$2x^4 + 8x^3 + 3x^3 + 4x + 1 = 0$$ given that the sum of two of the roots is zero. 2. **Simplify the polynomial:** Combine