Question

In the complex numbers, where $i=\sqrt{-1}$, the conjugate of any value $a+bi$ is $a-ib$. What is the result when you multiply $2+7i$ by its conjugate?

• A. $45$
• B. $-45$
• C. $45i$
• D. $53$
• E. $53i$

Answer 1

The correct option is D $53$

Conjugate of $2+7i$ is $2-7i$
$(2+7i)\times (2-7i)=2^2-(7i{)}^2$

$=4-49(-1)$

$=4+49$

$=53$