in it's simplest form square root everything to get:
a+b=8
i.e. a=8-b or b=8-a
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a2
The reciprocal of a + bi is a - bi:1/(a + bi) since the conjugate is a - bi:= 1(a - bi)/[(a + bi)(a - bi)]= (a - bi)/[a2 - (b2)(i2)] since i2 equals to -1:= (a - bi)/(a2 + b2) since a2 + b2 = 1:= a - bi/1= a - bi
b2 + 16b + 64 can be factorized to (b+8)(b+8). If they were equal to zero as in b2 + 16b + 64=0 then b = -8.
a right triangle
Pythagorean Theorem