Question #27e2b

3 Answers
Feb 5, 2018

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

Feb 5, 2018

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

Feb 5, 2018

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