Thread: Real and Imaginary function

Our function is h(z) = Re (z) / Im (z)
I am to find the values when z = i and z = (5 - 2i)/(2 - i)

I am totally confused by the Re and Im. Since if z is real how can it be equal to i or anything with i in it????

If I put i/i and then to clear i out of denominator I multiple by -i/-i then I get - i^2/ -i^2 which is 1. I know I am making a mistake because the answer is suppose to be 0. Is that because the numerator has to be 0 since z = i is not real???

If I use the other value for z I should get a value of 12 but again, I get 1 so I am not understanding the question. Any assistance would be much appreciated. Frostking

Originally Posted by Frostking

Our function is h(z) = Re (z) / Im (z)
I am to find the values when z = i and z = (5 - 2i)/(2 - i)

I am totally confused by the Re and Im. Since if z is real how can it be equal to i or anything with i in it????

If I put i/i and then to clear i out of denominator I multiple by -i/-i then I get - i^2/ -i^2 which is 1. I know I am making a mistake because the answer is suppose to be 0. Is that because the numerator has to be 0 since z = i is not real???

If I use the other value for z I should get a value of 12 but again, I get 1 so I am not understanding the question. Any assistance would be much appreciated. Frostking

Who says z is real? If z = i then Re(z) = 0 and Im(z) = 1, so

h(i) = 0, and if z = (5 - 2i)/(2 - i) = (12 + i)/5 = (12/5) + (1/5)i, then

h(z) = (12/5)/(1/5) = 12