write the expression as a complex number in standard form
1+2i
-----
3-8i
multiply top and bottom by (3-8i) and simplify.
you should get -13/73 + 14i/73
correct i just did this kind if stuff recently
To write the expression (1+2i) / (3-8i) as a complex number in standard form, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of 3-8i is 3+8i.
Now, let's proceed with the multiplication:
Numerator: (1+2i) * (3+8i)
Distributor: 1*(3+8i) + 2i*(3+8i)
Simplify: 3+8i+6i+16i^2
Rearrange: -13 + 14i
Denominator: (3-8i) * (3+8i)
Using the difference of squares: 3^2 - (8i)^2
Simplify: 9 - 64i^2
Substitute i^2 with -1: 9 - 64(-1)
Evaluate: 9 + 64
Now, the expression becomes:
(-13 + 14i) / (9 + 64)
Simplifying the numerator and denominator:
Numerator: -13 + 14i
Denominator: 73
So, the complex number in standard form is (-13 + 14i) / 73.