Verified Answer :

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The distance of a complex number a+bi from the origin on the complex plane is given by the formula:
\(\sqrt{a^2+b^2}\)

a.
\(2+15i \\ a=2 \\ b=15 \\ \Downarrow \\ d=\sqrt{2^2+15^2}=\sqrt{4+225}=\sqrt{229}\)

b.
\(17+i \\ a=17 \\ b=1 \\ \Downarrow \\ d=\sqrt{17^2+1^2}=\sqrt{289+1}=\sqrt{290}\)

c.
\(20-3i \\ a=20 \\ b=-3 \\ \Downarrow \\ d=\sqrt{20^2+(-3)^2}=\sqrt{400+9}=\sqrt{409}\)

d.
\(4-i \\ a=4 \\ b=-1 \\ \Downarrow \\ d=\sqrt{4^2+(-1)^2}=\sqrt{16+1}=\sqrt{17}\)

The answer is D.

Answer:

d 4-i

Step-by-step explanation:

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