Question

What values of a and b make this equation true?

Answer 1

Answer:

a = -4

b=-29

Step-by-step explanation:

Complex number:

First write the radicals in simplest form.

i² = -1

$\sf (4 + \sqrt{-49}) -2\left(\sqrt{(-4)^2}+\sqrt{-324}\right)=4 + \sqrt{49i^2} - 2\left(\\\sqrt{16}+\sqrt{324i^2}\right)$

                                                          $\sf =4 + \sqrt{7*7*i*i}-2\left(\sqrt{4*4}+\sqrt{18*18*i*i}\right)\\\\= 4 + 7i - 2(4 + 18i)\\\\= 4 + 7i - 2*4 - 2*18i\\\\= 4 + 7i -8-36i\\\\= 4 - 8 +7i - 36i\\\\= -4 - 29i$

   $\sf \boxed{a = -4 }\\\\\boxed{b=-29}$