Question

practice assignment 2.4 complex numbers
score: 180/250 answered: 18/25
question 19
perform the indicated operation & simplify. express the answer in terms of i (as a complex number).
(1 - 11i)² =
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Explanation:

Step1: Expand using \((a - b)^2=a^2-2ab + b^2\)

$$(1-11i)^2=1^2-2\times1\times11i+(11i)^2$$

Step2: Simplify each term

• For \(1^2\), we have \(1^2 = 1\).
• For \(-2\times1\times11i\), we get \(- 22i\).
• For \((11i)^2\), since \(i^2=-1\), then \((11i)^2=11^2\times i^2=121\times(-1)=-121\).

So, \(1^2-2\times1\times11i+(11i)^2=1-22i - 121\)

Step3: Combine like - terms

\(1-121-22i=-120 - 22i\)

Answer:

\(-120-22i\)