Problem 16
Question
Find each product and write the result in standard form. $$ (2+7 i)(2-7 i) $$
Step-by-Step Solution
Verified Answer
The product (2+7i)(2-7i) in standard form is 53.
1Step 1: Distribute
Firstly, distribute each term in the first complex number (2+7i) with each term in the second complex number (2-7i) separately: \[ (2 * 2) + (2 * -7i) + (7i * 2) + (7i * -7i) = 4 - 14i + 14i - 49i^2 \]
2Step 2: Simplify
Secondly, simplify the expression obtained after the distribution: \[ 4 - 49i^2 \]. The term \( - 14i + 14i \) simplify to zero and remember, the square of 'i', \(i^2\), is -1.
3Step 3: Final Calculation
Next, substitute \(i^2\) with -1 and do the calculation: \[ 4 - 49(-1) = 4 + 49 = 53 \]
Other exercises in this chapter
Problem 16
After a \(30 \%\) reduction, you purchase a dictionary for \(\$ 30.80 .\) What was the dictionary's price before the reduction?
View solution Problem 16
Solve and check each linear equation. $$\begin{aligned}&45-[4-2 y-4(y+7)]=\\\&-4(1+3 y)-[4-3(y+2)-2(2 y-5)]\end{aligned}$$
View solution Problem 16
Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1,0\) \(1,2,\) and 3. $$ y=x+2 $$
View solution Problem 17
Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$x-\sqrt{2 x+5}=5$$
View solution