Question

Which complex number has a distance of √17 from the origin on the complex plane?

a. 2 + 15i
b. 17 + i
c. 20 - 3i
d. 4 - i

Answer 1

d 4-i

Explanation:

Answer 2

The distance of a complex number a+bi from the origin on the complex plane is given by the formula:

`√(a^2+b^2)`

a.

`2+15i \\ a=2 \\ b=15 \\ \Downarrow \\ d=√(2^2+15^2)=√(4+225)=√(229)`

b.

`17+i \\ a=17 \\ b=1 \\ \Downarrow \\ d=√(17^2+1^2)=√(289+1)=√(290)`

c.

`20-3i \\ a=20 \\ b=-3 \\ \Downarrow \\ d=√(20^2+(-3)^2)=√(400+9)=√(409)`

d.

`4-i \\ a=4 \\ b=-1 \\ \Downarrow \\ d=√(4^2+(-1)^2)=√(16+1)=√(17)`

The answer is D.