Question

(Find the distance between each of the following complex numbers. Give your answers in simplified radical form, and show all your work.)

1.) -1+i and -3-4i
2.) 1+i and 7-2i
3.) -3+4i and -6-i
4.) -2+3i and 2-2i
5.) 3 and 5+i
6.) -4+5i and 2-i

Thank you!

Answer 1

Answer:

I) √29

ii) 3√5

iii) 5√5

iv) √41

v) √5

vi) 6√2

Step-by-step explanation:

1)

Given complex numbers    -1+i and -3-4i

The points are ( -1 , 1) and (-3 , -4 )

Distance formula

$\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^2 }$

= $\sqrt{(-4-(1) )^{2} +(-3 -(-1) )^2 } = \sqrt{25+4} =\sqrt{29}$

2)

Given complex numbers    1+i and 7-2i

The points are ( -3,4) and (-6,-1)

Distance formula

$\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^2 }$

$\sqrt{(-2-1 )^{2} +(7-1)^2 } = \sqrt{9+36} =\sqrt{45}= 3\sqrt{5}$

3)

Given complex numbers   -3 +4i and -6-i

The points are ( -3 ,4 ) and (-6 ,-1)

$\sqrt{(-1-4 )^{2} +(-6-4)^2 } = \sqrt{25+100} =\sqrt{125}= 5\sqrt{5}$

4)

Given complex numbers are -2+3i and 2-2i

The points are ( -2 ,3) and (2 , -2)

$\sqrt{(-2-3 )^{2} +(2+4)^2 } = \sqrt{25+36} =\sqrt{41}$



5)

Given complex numbers are 3 and 5+i

The points are( 3,0) and (5,1)

$\sqrt{(1-0 )^{2} +(5-3)^2 } = \sqrt{1+4} =\sqrt{5}$



6)

Given complex numbers are -4+5i and 2-i

The points are ( -4 ,5) and ( 2,-1)

$\sqrt{(-1-5 )^{2} +(2-(-4))^2 } = \sqrt{36+36} =\sqrt{72}= 6\sqrt{2}$