Conjugate equation

Find the numbers of a and b; if (a - bi) (3 + 5i) is the Conjugate of (-6 - 24i)

Correct answer:

a =  3
b =  -3

Step-by-step explanation:

(a − bi) (3 + 5i)  = conj(−6 − 24i) (a − bi) (3 + 5i)  = −6 + 24i 3a+5ai −3bi+5b  = −6 + 24i (3a+5b) +i(5a −3b)  = −6 + 24i  3a+5b=−6 5a−3b=24  3⋅ a+5⋅ b=−6 5⋅ a−3⋅ b=24  3a+5b=−6 5a−3b=24  Pivot:Row1↔Row2 5a−3b=24 3a+5b=−6  Row2−53​⋅ Row1→Row2 5a−3b=24 6.8b=−20.4  b=6.8−20.4​=−3 a=524+3b​=524+3⋅ (−3)​=3  a=3 b=−3

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