Given that the complex number 𝑍 is represented by the point negative four, negative four on the Argand diagram below, find the absolute value of 𝑍.
Now when it says to find the absolute value of 𝑍, absolute value just means the distance from zero. So we’re finding that distance. The absolute value of 𝑍 would be equal to negative four minus four 𝑖 as the complex number, because it would go left four on the real line and then down four on the imaginary line.
Essentially you’re using the Pythagorean theorem. So that distance would be negative four squared plus negative four squared will equal that distance squared. So we would just need to take the square root of it, which is the distance formula.
And negative four squared is 16. And 16 plus 16 could actually be written as 16 times two, which could be split up. And the square root of 16 is four. And the square root of two does not simplify. So our final answer is four square root two.