In the following applet, you can check the boxes to show the sum, product, and ratio (or quotient) of the complex numbers [i]z[/i][sub]1[/sub] and [i]z[/i][sub]2[/sub]. But first, I'd like you to leave those boxes unchecked, and focus just on the absolute value of the numbers.
How do we define the absolute value of a number?
If you were given a point on the Cartesian coordinate plane, one that was not on either axis, how would you calculate its distance from the origin?
[size=85][size=100]Set [i]z[/i][sub]1[/sub] to be 8+6i and [i]z[/i][sub]2[/sub] to be -4+3i. Note their respective absolute values. What relationship do the coefficients [i]a[/i] and [i]b[/i] have to the absolute value in each case?[/size][/size]
Based on your answer to the last question then, how is the absolute value of a complex number calculated? Does the quadrant in which the complex number falls affect the absolute value calculation? (In other words, would abs(3-i)=abs(-3+i)?)
You should now go to deltamath and complete the practice problems in the section "Finding the Modulus of a Complex Number".[br]Then try the problems in Section 5.4 of the textbook, on page 278: #64, 65, 66, 68, 70, 71, and 80-85 all