If ( a + i b ) 1 4 = 2 + 3 i , then 3 b - 2 a =

Question

If ( a + i b ) 1 4 = 2 + 3 i , then 3 b - 2 a =, - 22, - 122, - 598, - 698

MARKS App · Accepted Answer

Given ( a + i b ) 1 4 = 2 + 3 i ⇒ ( a + i b ) = 2 + 3 i 4 ⇒ a + i b = 2 + 3 i 2 2 = 4 + 9 i 2 + 12 i 2 = 4 - 9 + 12 i 2 = 12 i - 5 2 = 144 i 2 + 25 - 120 i = - 119 - 120 i Comparing with a + i b a = - 119 , b = - 120 Therefore 3 b - 2 a = 3 ( - 120 ) - 2 ( - 119 ) = - 122

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