Chapter 4: Q. 1 (page 215)

Find the sum and the product of the complex numbers $3 - 2 i$ and $- 3 + 5 i$ .

Short Answer

Expert verified

The sum and the product of the complex numbers are $0 - 7 i$ and $- 19 - 9 i$ respectively.

Step by step solution

Step 1. Given Information

Two complex numbers are given as $3 - 2 i$ and $- 3 - 5 i$ .

Step 2. Concept of the sum of and product of two complex numbers

Sum of two complex numbers $a + i b$ and $c + i d$ can be calculated as

role="math" localid="1646294259645" $(a + i b) + (c + i d) = (a + c) + i (b + d)$

Product of two complex numbers $a + i b$ and $c + i d$ can be calculated as

$(a + i b) (c + i d) = a c - b d + i (b c + a d)$

Step 3. Simplification

Add the complex numbers as shown.

$3 - 2 i + (- 3 - 5 i) = (3 - 3) + i (- 2 - 5) = 0 - 7 i$

Multiply the complex numbers as shown.

$(3 - 2 i) (- 3 - 5 i) = (3) (- 3) + (- 5 i) (- 2 i) + (3) (- 5 i) + (- 3) (- 2 i) = - 9 + 10 i^{2} - 15 i + 6 i = - 9 - 10 - 9 i = - 19 - 9 i$

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Find the sum and the product of the complex numbers $3 - 2 i$ and $- 3 + 5 i$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept of the sum of and product of two complex numbers

Step 3. Simplification

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Find the sum and the product of the complex numbers3-2iand -3+5i.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept of the sum of and product of two complex numbers

Step 3. Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Statistics

Mechanics Maths

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

Find the sum and the product of the complex numbers $3 - 2 i$ and $- 3 + 5 i$ .