 Write the expression as a complex number in standard form.  1.) (9 + 8i) + (8 – 9i)  2.) (-1 + i) – (7 – 5i)  3.) (8 – 5i) – ( i) Warm Up

4.6 Perform Operations with Complex Numbers, part II Algebra II

 Multiply and divide complex numbers.  Plot complex numbers.  Find the absolute value of complex numbers. Objectives

 Write the expression as a complex number in standard form.  A.) -5i(8 – 9i)  B.) (-8 + 2i)(4 – 7i) Example 3 – Multiply complex numbers

 Two complex numbers of the form a + bi and a – bi are called complex conjugates.  The product of complex conjugates is always a real number.  Ex. (2 + 4i)(2 – 4i) Complex conjugates

 Write the quotient in standard form.  3 + 4i 5 - i Example 4 – Divide complex numbers

 The complex plane has a horizontal axis (real axis) and a vertical axis (imaginary axis).  Plot the complex numbers in the same complex plane.  A.) 4 + 2i B.) i C.) -4i D.) 2 – 2i Example 5 – Plot complex numbers

 The absolute value of a complex number z = a + bi, denoted |z|, is a nonnegative real number defined as |z| = √a 2 + b 2 Absolute Value of a Complex Number

 Find the absolute value of 5 – 12i and 17i Example 7 – Find the absolute value of complex numbers

 Evaluate each expression if X = 5 – 8i and Y = i. Write your answer as a complex number in standard form.  1.) X – Y  2.) X * Y  3.) X + Y Warm Up

 Pg. 280 (22 – 33 all, 34 – 48 even) Assignment