Question 4 of 28beginner🔧 ApplyNumerical1 mark

Express the following complex number in the form a+iba + ib: 3(7+i7)+i(7+i7)3(7 + i7) + i(7 + i7)

Correct Answer

14 + 28i

Exercise: EXERCISE 4.1 | Q: 4 | (Page 7)
For More Understanding

Explanation

This question is from Exercise 4.1, Question 4. It tests the basic operations on complex numbers - multiplication and addition. Students need to apply the distributive property and use the fundamental property i² = -1 to simplify the expression.

Solution Steps

  1. Step 1: Expand the first term: 3(7 + i7) = 3×73 \times 7 + 3 × i7 = 21 + 21i

  2. Step 2: Expand the second term: i(7 + i7) = i × 7 + i × i7 = 7i + 7i²

  3. Step 3: Since i² = -1, substitute: 7i + 7i² = 7i + 7(-1) = 7i - 7 = -7 + 7i

  4. Step 4: Add both results: (21 + 21i) + (-7 + 7i) = (21 - 7) + (21 + 7)i = 14 + 28i

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