Question

Simplify the expression the root of negative one all over the quantity of four minus three i minus the quantity of two plus five i.

Really don't get this please help.

Answer 1

We will break this down into its parts:
We know that this is a fraction where the numerator is √(-1) = i
The denominator:
4 - 3i - (2 + 5i); we put 2 + 5i in brackets because we are to subtract its quantity.
Simplifying the denominator:
4 - 3i - 2 - 5i
= 2 - 8i
Now, we write the expression in fractional form:
i / (2 - 8i)
To remove an imaginary number from the denominator, we multiply and divide by its conjugate. The conjugate of a + bi is a - bi
i(2 + 8i) / (2² - (8i)²)
= (-8 + 2i) / (4 + 64)
= -2/17 + i/34