I’m trying to figure out
-5+i / 2i
I went through it by myself and got (0.5+2.5i) but I’m not sure I did it correctly? Can anybody verify my answer or tell me what I might have done wrong? Thank you!
I guess maybe you mean
(-5 + i) / 2i ????
-5/2i + i/2i
-2.5 i/i^2 + .5
but i^2 = -1
I also get .5 + 2.5 i
Yes, thank you!! I’m just a little nervous with imaginary numbers at times haha. I appreciate it.
To simplify the expression (-5+i) / (2i), you can use a technique called rationalizing the denominator. This involves multiplying the numerator and denominator by the conjugate of the denominator, which is the complex number with the same real part but the opposite sign for the imaginary part.
In this case, the conjugate of 2i is -2i. So, you can multiply both the numerator and denominator by -2i:
((-5+i) / (2i)) * (-2i/-2i)
= ( (-5+i) * (-2i) ) / (2i * -2i)
= (10i - 2i^2) / (-4i^2)
Now, simplify further by recognizing that i^2 is equal to -1:
(10i - 2(-1)) / (-4(-1))
= (10i + 2) / 4
Finally, divide both the numerator and the denominator by 2:
10i/4 + 2/4
= 5i/2 + 1/2
= (1/2) + (5/2)i
So, the simplified form of (-5+i) / (2i) is (1/2) + (5/2)i.
Based on your calculation, it seems like you incorrectly added the real and imaginary parts together. The correct answer is (1/2) + (5/2)i, not (0.5 + 2.5i).