Question

The product of (3+2i) and a complex number is (17+7i) What is the complex number.

Answer 1

The question is asking us to find the complex number such that: ( 3 + 2 i ) * x = 17 + 7 i. We know that i^ 2 = - 1. x = ( 17 + 7 i ) / ( 3 + 2 i ) . We have to multiply the numerator and the denominator by ( 3 - 2 i ). Then: x = ( 17 + 7 i ) * ( 3 - 2 i ) / ( 9 - 4 i^2 ) = ( 51 - 34 i + 21 i - 14 i^2 ) / ( 9 + 4 ) = ( 51 + 14 - 13 i ) / 13 = ( 65 - 13 i ) / 13 = 65 / 13 - 13 i / 13 = 5 - i. Answer: The complex number is 5 - i.