which complex number has an absolute value of 5?\n○ -3+4i\n○ 2+3i\n○ 7-2i\n○ 9+4i

Answer:

A. $-3+4i$

Explanation:

Step1: Understand the absolute value of a complex number

The absolute value (or modulus) of a complex number $z = a + bi$ is given by the formula $|z| = \sqrt{a^2 + b^2}$. We need to find which of the given complex numbers has an absolute value of 5.

Step2: Calculate the absolute value for each option

Option A: $-3+4i$

Here, $a = -3$ and $b = 4$. $|-3+4i| = \sqrt{(-3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.

Option B: $2+3i$

Here, $a = 2$ and $b = 3$. $|2+3i| = \sqrt{(2)^2 + (3)^2} = \sqrt{4 + 9} = \sqrt{13}$.

Option C: $7-2i$

Here, $a = 7$ and $b = -2$. $|7-2i| = \sqrt{(7)^2 + (-2)^2} = \sqrt{49 + 4} = \sqrt{53}$.

Option D: $9+4i$

Here, $a = 9$ and $b = 4$. $|9+4i| = \sqrt{(9)^2 + (4)^2} = \sqrt{81 + 16} = \sqrt{97}$.

Step3: Compare the results with the required absolute value

Only the complex number $-3+4i$ has an absolute value of 5.