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Chapter 4: Q. 1 (page 215)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information

Two complex numbers are given as3-2iand-3-5i.

02

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

Sum of two complex numbers a+iband c+idcan be calculated as

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

Product of two complex numbers a+iband c+idcan be calculated as

(a+ib)(c+id)=ac-bd+i(bc+ad)

03

Step 3. Simplification 

Add the complex numbers as shown.

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

Multiply the complex numbers as shown.

3-2i-3-5i=3-3+-5i-2i+3-5i+-3-2i=-9+10i2-15i+6i=-9-10-9i=-19-9i

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