Question

Write the quotient in standard form.
10 − 15i
1 − 2i

Answer 1

8 +i

Explanation:

You want the quotient (10 -15i)/(1 -2i).

Simplify

The rational expression can have the denominator made real by multiplying numerator and denominator by the conjugate of the denominator:

`(10-15i)/(1-2i)=((10-15i)(1+2i))/((1-2i)(1+2i))=(10+20i-15i-30i^2)/(1-4i^2)\\\\\\=(40+5i)/(5)=\boxed{8+i}`

__

Additional comment

Expressions involving i can be treated as though i were a variable. All instances of i² can be replaced with -1.

<95141404393>