Trigonometric Form of Complex Numbers Lesson 5 2

Trigonometric Form of Complex Numbers Lesson 5. 2

Graphical Representation of a Complex Number ¡ Graph in coordinate plane l Called the complex plane l Horizontal axis is the real axis l Vertical axis is the imaginary axis 3 + 4 i • -2 + 3 i • • -5 i 2

Absolute Value of a Complex Number ¡ Defined as the length of the line segment l l ¡ From the origin To the point Calculated by using Pythagorean Theorem 3 + 4 i • 3

Find That Value, Absolutely ¡ Try these l l Graph the complex number Find the absolute value 4

Trig Form of Complex Number ¡ ¡ Consider the graphical representation We note that a right triangle is formed a + bi • r b θ a How do we determine θ? 5

Trig Form of Complex Number ¡ Now we use and substitute into z = a + bi ¡ Result is ¡ Abbreviation is often 6

Try It Out ¡ Given the complex number -5 + 6 i l l l ¡ Write in trigonometric form r=? θ=? Given z = 3 cis 315° l l Write in standanrd form r=? a=? b=? 7

Product of Complex Numbers in Trig Form ¡ Given ¡ It can be shown that the product is l l Multiply the absolute values Add the θ's 8

Quotient of Complex Numbers in Trig Form ¡ Given ¡ It can be shown that the quotient is 9

Try It Out ¡ ¡ Try the following operations using trig form Convert answers to standard form 10

Assignment Lesson 5. 2 ¡ Page 349 ¡ Exercises 1 – 61 EOO ¡ 11