SOLUTION: what is the reciprocal of 3-7i what is the reciprocal of 1 + 6i what is the reciprocal of -1-i

 

Hi,

what is the reciprocal of 3-7i 

1/(3-7i) = (3+7i)/(3-7i)(3+7i) = (3+7i)/(9+49) = (3+7i)/58 

Multiplying both numerator and denominator by (3+7i) Note: i^2 = -1



what is the reciprocal of 1 + 6i = 1/(1+6i)

Multiply both numerator and denominator by (1-6i)to simplify

what is the reciprocal of -1-i =  -1/(1+i)

Multiply both numerator and denominator by (1-i)to simplify



Multiplying Numerator and Dnominator by the conjugate of the Denominator:

puts the reciprocal in the desired format

F	First terms

O	Outside terms

I	Inside terms

L	Last terms