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## Trigonometric Form of Complex Numbers

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**Trigonometric Form of Complex Numbers**Lesson 5.2**Graphical Representation of a Complex Number**• Graph in coordinate plane • Called the complex plane • Horizontal axisis the real axis • Vertical axis is the imaginaryaxis 3 + 4i• -2 + 3i• • -5i**Absolute Value of a Complex Number**• Defined as the length of the line segment • From the origin • To the point • Calculated byusing PythagoreanTheorem 3 + 4i•**Find That Value, Absolutely**• Try these • Graph the complex number • Find the absolute value**Trig Form of Complex Number**• Consider the graphical representation • We note that a righttriangle is formed a + bi• r b θ a How do we determine θ?**Trig Form of Complex Number**• Now we use and substitute into z = a + bi • Result is • Abbreviation is often**Try It Out**• Given the complex number -5 + 6i • Write in trigonometric form • r = ? • θ = ? • Given z = 3 cis 315° • Write in standanrd form • r = ? • a = ? • b = ?**Product of Complex Numbers in Trig Form**• Given • It can be shown that the product is • Multiply the absolute values • Add the θ's**Quotient of Complex Numbers in Trig Form**• Given • It can be shown that the quotient is**Try It Out**• Try the following operations using trig form • Convert answers to standard form**Assignment**• Lesson 5.2 • Page 349 • Exercises 1 – 61 EOO