Question

which of the following options is equivalent to $z_1cdot z_2$? select all that apply.
$z_1 = 2sqrt{5}-sqrt{3}i$
$z_2 = 2sqrt{5}+sqrt{3}i$
$z_1cdot z_2 = 23 + 0i$
$z_1cdot z_2 = 23 - 0i$
$z_1cdot z_2 = 4sqrt{25}+2isqrt{15}-2isqrt{15}-(sqrt{3}i)^2$
$z_1cdot z_2 = 4sqrt{5}+2isqrt{15}-2isqrt{15}-(3cdot i^2)$
$z_1cdot z_2 = 20 + 2isqrt{15}-2isqrt{15}-(3cdot - 1)$
$z_1cdot z_2 = 4cdot5+2isqrt{15}-2i15-(3cdot i^2)$

Explanation:

Explicación:

Paso1: Multiplicar los números complejos

$$z_1\cdot z_2=(2\sqrt{5}-\sqrt{3}i)(2\sqrt{5}+\sqrt{3}i)$$
Usando la fórmula $(a - b)(a + b)=a^2 - b^2$, donde $a = 2\sqrt{5}$ y $b=\sqrt{3}i$.

Paso2: Expandir la expresión

$$z_1\cdot z_2=(2\sqrt{5})^2-(\sqrt{3}i)^2$$
$$z_1\cdot z_2 = 4\times5-3i^2$$

Paso3: Sustituir $i^2=-1$

$$z_1\cdot z_2=20 - 3\times(-1)$$
$$z_1\cdot z_2=20 + 3=23+0i=23 - 0i$$
También, si se expande directamente:
$$z_1\cdot z_2=4\sqrt{25}+2i\sqrt{15}-2i\sqrt{15}-(\sqrt{3}i)^2$$
$$z_1\cdot z_2 = 4\times5+2i\sqrt{15}-2i\sqrt{15}-(3\cdot i^2)$$
$$z_1\cdot z_2=20 + 2i\sqrt{15}-2i\sqrt{15}-(3\cdot(-1))$$

Respuesta:

• $z_1\cdot z_2 = 23+0i$
• $z_1\cdot z_2 = 23 - 0i$
• $z_1\cdot z_2 = 4\sqrt{25}+2i\sqrt{15}-2i\sqrt{15}-(\sqrt{3}i)^2$
• $z_1\cdot z_2 = 4\sqrt{5}+2i\sqrt{15}-2i\sqrt{15}-(3\cdot i^2)$
• $z_1\cdot z_2 = 20 + 2i\sqrt{15}-2i\sqrt{15}-(3\cdot(-1))$

Answer:

Explicación:

Paso1: Multiplicar los números complejos

$$z_1\cdot z_2=(2\sqrt{5}-\sqrt{3}i)(2\sqrt{5}+\sqrt{3}i)$$
Usando la fórmula $(a - b)(a + b)=a^2 - b^2$, donde $a = 2\sqrt{5}$ y $b=\sqrt{3}i$.

Paso2: Expandir la expresión

$$z_1\cdot z_2=(2\sqrt{5})^2-(\sqrt{3}i)^2$$
$$z_1\cdot z_2 = 4\times5-3i^2$$

Paso3: Sustituir $i^2=-1$

$$z_1\cdot z_2=20 - 3\times(-1)$$
$$z_1\cdot z_2=20 + 3=23+0i=23 - 0i$$
También, si se expande directamente:
$$z_1\cdot z_2=4\sqrt{25}+2i\sqrt{15}-2i\sqrt{15}-(\sqrt{3}i)^2$$
$$z_1\cdot z_2 = 4\times5+2i\sqrt{15}-2i\sqrt{15}-(3\cdot i^2)$$
$$z_1\cdot z_2=20 + 2i\sqrt{15}-2i\sqrt{15}-(3\cdot(-1))$$

Respuesta:

• $z_1\cdot z_2 = 23+0i$
• $z_1\cdot z_2 = 23 - 0i$
• $z_1\cdot z_2 = 4\sqrt{25}+2i\sqrt{15}-2i\sqrt{15}-(\sqrt{3}i)^2$
• $z_1\cdot z_2 = 4\sqrt{5}+2i\sqrt{15}-2i\sqrt{15}-(3\cdot i^2)$
• $z_1\cdot z_2 = 20 + 2i\sqrt{15}-2i\sqrt{15}-(3\cdot(-1))$