Question

If the statement is true, type true in the space provided. If it is false, replace the underline word(s) in the word(s) that will make the statement true.

Answer 1

False; sum

Step-by-step explanation

Let a+ib be a complex number. Then, its conjugate is a-ib. Multiply them,

`(a+ib)(a-ib)=a^2-a\cdot ib+a\cdot ib-i^2b^2=a^2-(-1)b^2=a^2+b^2`

Hence, when we multiply two conjugates the result is the sum of the squares of the real and imaginary parts. So the statement is false. We have to replace the word difference with sum to make the statement true.