Question

Find the complex conjugate of (2+5i)^2

Answer 1

Complex numbers

• Complex numbers are the numbers that expressed in the form a+ib.
• Here a and b are real numbers and i is a complex number
• The value of 'i' is $\bf\sqrt{-1}$

Complex Conjugate

Complex conjugate means reflecting the complex plane in the real line.

• The complex conjugate of i is denoted by -i.

Given, $(2+5i)^{2}$

Let us expand this using,

               $(a+b)^{2} =a^{2}+b^2+2ab$

              $(2+5i)^{2} = 4+25\,i^2+2\times5i\times2$

We know that,   $i =\sqrt{-1}$   ⇒  $i^2 = -1$

       ⇒ $(2+5i)^{2} = 4+25(-1)+2\times5i\times2$

           $(2+5i)^{2} =-21+20i$

∴ The complex conjugate of   $\bf(2+5i)^{2} =-21+20i$  is $\bf-21 - 20i$

(#SPJ3)

Answer 2

Step-by-step explanation:

here is the answer for (2+5i)^2