Question

lesson: multiplying complex numbers
multiply: 5i(2 - 10i) (type your final answer in the box. do not put any spaces)

Explanation:

Step1: Apply distributive property

Use the distributive property \( a(b + c)=ab+ac \) (here \( a = 5i \), \( b = 2 \), \( c=- 10i \)):
\( 5i(2 - 10i)=5i\times2-5i\times10i \)

Step2: Simplify each term

Simplify \( 5i\times2 = 10i \) and \( 5i\times10i=50i^{2} \). Recall that \( i^{2}=- 1 \), so \( 50i^{2}=50\times(-1)=-50 \).

Step3: Combine terms

Now we have \( 10i-50 \). Rearranging in standard complex number form (\( a + bi \)), we get \( -50 + 10i \).

Answer:

-50+10i