Question

I think it's B, but I'm not positive!

Which complex number has an absolute value of 5?
a) –3 + 4i
b) 2 + 3i
c) 7 – 2i
d) 9 + 4i

Answer 1

@mtbender74

Answer 2

Remember, to find the absolute value of a complex number (say \(a+bi\)), you need to look at \(\sqrt{a^2+b^2}\). So for the second option, can you tell me what \(\sqrt{a^2+b^2}\) is?

Answer 3

3.6?

Answer 4

Notice how \(3.6\neq5\). That means that the absolute value of \(2+3i\) is NOT 5. Can you find another option that is 5?

Answer 5

Ohhh. Okay, I get it now. I just calculated all of them though, and none of them equaled 5, unless I'm calculating wrong. But the one that was the closest to 5 was C; I got 6.7

Answer 6

One of them is actually equal to 5. Let's go through them in reverse order.

Answer 7

D. \(9+4i\):\[|9+4i|=\sqrt{9^2+4^2}=\sqrt{81+16}=\sqrt{97}\neq5\]
C. \(7-2i\):\[|7-2i|=\sqrt{7^2+(-2)^2}=\sqrt{49+4}=\sqrt{53}\neq5\]
B. \(2+3i\):\[|2+3i|=\sqrt{2^2+3^2}=\sqrt{4+9}=\sqrt{13}\neq5\]
A. \(-3+4i\):\[|-3+4i|=\sqrt{(-3)^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\]

Answer 8

Remember that when you square negative numbers you still get a positive number.

Answer 9

Oh, okay! I was calculating the equations with negative numbers wrong, that's why I couldn't find the answer. I get it 100% now though. Thank you so much.

Answer 10

You'rewelcome.