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Can anyone help me with this true or false question

Can anyone help me with this true or false question-example-1
User Hanna
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ANSWER

A. True

Step-by-step explanation

Let the complex number be z = a+ ib, so its complex conjugate is z* = a - ib, where a and b are real numbers. Let's find the product,

The product is,


(a+ib)(a-ib)=a\cdot a-a\operatorname{\cdot}ib+ib\operatorname{\cdot}a-ib\operatorname{\cdot}ib

Solve the products,


(a+ib)(a-ib)=a^2-iab+iab-i^2b^2

Simplify: note that the second and third terms are opposites, so they cancel out. Remember that i² is equal to -1,


(a+ib)(a-ib)=a^2+0-(-1)b^2=a^2+b^2

Since a and b were real numbers, then the sum of their squares is also a real number.

Hence, this statement is true.

Can anyone help me with this true or false question-example-1
User Caity
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