Question

Question #27e2b

Answer 1

`z_1/z_2=2+i`

Explanation:

We need to calculate
`z_1/z_2=(4-3i)/(1-2i)`

We can't really do much because the denominator has two terms in it, but there is a trick we can use. If we multiply the top and bottom by the conjugate, we'll get an entirely real number on the bottom, which will let us calculate the fraction.

`(4-3i)/(1-2i)=((4-3i)(1+2i))/((1-2i)(1+2i))=(4+8i-3i+6)/(1+4)=`

`=(10+5i)/5=2+i`

So, our answer is `2+i`

Answer 2

The answer is `=2+i`

Explanation:

The complex numbers are

`z_1=4-3i`

`z_2=1-2i`

`z_1/z_2=(4-3i)/(1-2i)`

`i^2=-1`

Multiply the numerator and denominator by the conjugate of the denominator

`z_1/z_2=(z_1*barz_2)/(z_2*barz_2)=((4-3i)(1+2i))/((1-2i)(1+2i))`

`=(4+5i-6i^2)/(1-4i^2)`

`=(10+5i)/(5)`

`=2+i`

Answer 3

`2+i`

Explanation:

`z_1/z_2=(4-3i)/(1-2i)`

`"multiply numerator/denominator by the "color(blue)"complex conjugate"" of the denominator"`

`"the conjugate of "1-2i" is "1color(red)(+)2i`

`color(orange)"Reminder"color(white)(x)i^2=(sqrt(-1))^2=-1`

`rArr((4-3i)(1+2i))/((1-2i)(1+2i))`

`"expand factors using FOIL"`

`=(4+5i-6i^2)/(1-4i^2)`

`=(10+5i)/5=2+i`