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Chapter 6: Problem 10

Plot each complex number and find its absolute value. $$z=-3-4 i$$

Short Answer

Expert verified
The absolute value of the complex number \(-3-4i\) is 5.

Step by step solution

01

Representation of the complex number on the complex plane

The number on the complex plane can be represented as a point \(-3, -4\), where the x-axis represents the real part of the number and the y-axis represents the imaginary part of the number.
02

Absolute value calculation

The absolute value (or modulus) of a complex number \(z = x + yi\) is given by the formula \[|z| = \sqrt{x^2 + y^2}\]. In this case, \(x = -3\) and \(y = -4\). Plugging these values into the formula gives: \[|-3-4i| = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5\].
03

Conclusion

The complex number \(-3-4i\) has been represented in the complex plane and its absolute value is 5.

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