Question

Write the conjugate of (6+5i)^2

Answer 1

${(6 + 5i)}^{2} = {6}^{2} + 2 \times 6 \times 5i + {(5i)}^{2} \\ = 36 + 60i - 25 \\ = 11 + 60i \\ therefore \: \: conjugate \: \: of \: \: {(6 + 5i)}^{2} \\ = conjugate \: \: of \: \: 11 + 60i \\ = 11 - 60i$

Answer 2

Answer:

The conjugate of the given complex function, $(6+5i)^2$ , is found to be $11-60i$.

Step-by-step explanation:

The complex function given to us is: $(6+5i)^{2}$

Simplifying the function by using the identity- $(a+b)^{2}=a^2+b^2+2ab$, we get:

$(6+5i)^2=(6)^2+(5i)^2+2(5i)(6)$

We know that for any complex number, $i^2=-1$,

Using this identity, we can say:

$(6+5i)^2=36-25+60i$

or we can say:

$(6+5i)^2=11+60i$

Let the conjugate of the given function be: $x$,

Now, finding the conjugate of the obtained simplified complex function by changing the sign of $i$, we get:

$x=11-60i$