Simplify Write your answer in the form of abi where a and b

Simplify. Write your answer in the form of a+bi, where a and b are real numbers. 8-i/-4+7i

Solution

On multiplying both the sides of the given fraction by 1/ ( -4 - 7i) ,we have (8 - i) / ( -4 + 7i) = ( 8 - i)( -4 - 7i) /[( -4 + 7i)( -4 -7i)] = ( - 32 + 4i - 56i + 7i² )  /[ ( -4)² - (7i)²] = ( -39 - 52 i)/ ( 16+ 49) = - ( 39 + 52i)/65 = - ( 3 + 4i)/5 = -3/5 -( 4/5) i ( as i² = -1)