5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.

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Presentation transcript:

5.9 Complex Numbers Alg 2

Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.

Express the number in terms of i. Factor out –1. Product Property. Simplify. Express in terms of i.

Express the number in terms of i.

Answer: = 6 Simplify.

Simplify Multiplying powers Power of a Power Answer:

Solve the equation. Take square roots. Express in terms of i. Check x 2 = –144 –144 (12i) 2 144i 2 144(–1) x 2 = –144 – (–1) 144i 2 (–12i) 2

x = 0 Solve the equation. Add –48 to both sides. Take square roots. Express in terms of i. x 2 = –48 Checkx = (48)i (–1) + 48

Every complex number has a real part a and an imaginary part b. A complex number is written in the form a + bi, where a and b are real numbers and i =. Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.

Find the values of x and y that make the equation 4x + 10i = 2 – (4y)i true. Equate the real parts. 4x + 10i = 2 – (4y)i Real parts Imaginary parts 4x = 2 Solve for y. Solve for x. Equate the imaginary parts. 10 = –4y

Find the values of x and y that make each equation true. Equate the real parts. Real parts Imaginary parts –8 = 5x Solve for y. Solve for x. Equate the imaginary parts. –8 + (6y)i = 5x – i

The solutions and are related. These solutions are a complex conjugate pair. Their real parts are equal and their imaginary parts are opposites.

and are conjugates. Multiply. Answer: Standard form Simplify.

Multiply. Answer: Standard form Multiply by