Question

1. simplify. (1/2 point each) (2i√5)^2
2. (√4/i)^2
3. write the radical expression for the complex number given. (1/2 point)

4 + 16i

1. add: (5 - i) + (1 + 3i)
2. subtract: (2 - 7i) - (5 - 3i)
3. multiply: (4 + 5i)(2 + i)
4. multiply: (3 + 2i)^2

learning goal from lesson 3.2
i can apply the commutative, associative, distributive properties to complex numbers in order to add, subtract, and multiply.
how i did (circle one)
i got it!
im still learning it.

Explanation:

5.

Step1: Square the coefficient and the square - root term separately.

$(2\sqrt{5})^2=2^2\times(\sqrt{5})^2$

Step2: Calculate the squares.

$2^2 = 4$ and $(\sqrt{5})^2=5$, then $4\times5 = 20$

Step1: First, simplify the square - root inside the parentheses. $\sqrt{4}=2$.

$(\frac{\sqrt{4}}{2})^2=(\frac{2}{2})^2$

Step2: Calculate the fraction and then square it.

$\frac{2}{2}=1$, and $1^2 = 1$

Step1: Recall that a complex number is in the form $a + bi$. Here, the given number $4+16i$ is already in the standard form of a complex number.

Answer:

$20$

6.