Question

write each expression in the form $a + bi$, where $a$ and $b$ are real numbers.

1. $4i \cdot 3i$
2. $4i \cdot -3i$
3. $-2i \cdot -5i$
4. $-5i \cdot 5i$
5. $(-5i)^2$

Explanation:

Step1: Aplicar propiedad $i^2=-1$

$4i \cdot 3i = (4 \cdot 3) \cdot i^2 = 12 \cdot (-1) = -12$

Step2: Aplicar propiedad $i^2=-1$

$4i \cdot (-3i) = (4 \cdot (-3)) \cdot i^2 = -12 \cdot (-1) = 12$

Step3: Aplicar propiedad $i^2=-1$

$-2i \cdot (-5i) = ((-2) \cdot (-5)) \cdot i^2 = 10 \cdot (-1) = -10$

Step4: Aplicar propiedad $i^2=-1$

$-5i \cdot 5i = ((-5) \cdot 5) \cdot i^2 = -25 \cdot (-1) = 25$

Step5: Expandir y usar $i^2=-1$

$(-5i)^2 = (-5)^2 \cdot i^2 = 25 \cdot (-1) = -25$

Answer:

1. $-12 + 0i$ o simplemente $-12$
2. $12 + 0i$ o simplemente $12$
3. $-10 + 0i$ o simplemente $-10$
4. $25 + 0i$ o simplemente $25$
5. $-25 + 0i$ o simplemente $-25$