Complex Numbers and Vector Analysis

Complex numbers are unique as they integrate both real and imaginary numbers. They are typically denoted as a+bi, where 'a' and 'b' are real numbers, and 'i' represents the square root of -1. On the other hand, Vector Analysis is a mathematical discipline that handles quantities which possess both magnitude and direction. Examples of these quantities include force or velocity. These are frequently depicted graphically as arrows.

Finding All Complex Number Solutions

Simplify, if possible. \[ \sqrt{-12} \] \[ \sqrt{-12}= \] (Simplify your answer. Type an exact answer, using radicals and $i$ needed.)

Rationalizing with Complex Conjugates

Express the radical using the imaginary unit, $i$. Express your answer in simplified form. \[ \pm \sqrt{-44}= \pm \] Stuck? Review related articles/videos or use a hint.

Vector Arithmetic

Perform the operation and simplify the result. \[ 14-(8+3 i) \] type your answer...

Finding the Complex Conjugate

Given $z=7+3 i$, find the product $z \cdot \bar{z}$

Finding the Magnitude of a Complex Number

Find the magnitude of the complex number \( z = 3 + 4i \).