Math Problem Statement

Solution

The problem involves finding the magnitude of the complex number z=1iz = -1 - i.

The magnitude z|z| of a complex number z=a+biz = a + bi is given by: z=a2+b2|z| = \sqrt{a^2 + b^2}

For the given complex number z=1iz = -1 - i:

  • The real part a=1a = -1
  • The imaginary part b=1b = -1

Substituting these values into the formula: z=(1)2+(1)2|z| = \sqrt{(-1)^2 + (-1)^2} z=1+1|z| = \sqrt{1 + 1} z=2|z| = \sqrt{2}

Therefore, the magnitude of zz is: z=2|z| = \sqrt{2}

So, the correct option is C.

Do you want more details or have any questions?

Here are 5 more questions you might want to ask:

  1. How do you add and subtract complex numbers?
  2. How do you multiply and divide complex numbers?
  3. What is the geometric interpretation of complex numbers?
  4. How do you convert a complex number to polar form?
  5. What are the properties of complex conjugates?

Tip: When dealing with complex numbers, always remember that their magnitude represents the distance from the origin in the complex plane, which can be calculated using the Pythagorean theorem.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Complex Numbers
Magnitude of Complex Numbers
Pythagorean Theorem

Formulas

Magnitude of a complex number |z| = sqrt(a^2 + b^2)

Theorems

-

Suitable Grade Level

High School