Question

What values of a and b make this equation true?

Answer 1

a = -4

b=-29

Explanation:

Complex number:

First write the radicals in simplest form.

i² = -1

`\sf (4 + √(-49)) -2\left(√((-4)^2)+√(-324)\right)=4 + √(49i^2) - 2\left(\\√(16)+√(324i^2)\right)`

`\sf =4 + √(7*7*i*i)-2\left(√(4*4)+√(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}`