Warm Up for 1.1 in Math 2 2.3x = 23 ANSWER 5, – 5 1. Simplify 3 4 – 5 Solve the equation (x + 7) 2 = 16 Solve the equation. ANSWER – , –7 – Three times the square of a number is 15. What is the number? – 5, 5 ANSWER

1.1 Writing Complex Numbers Purple Math 2 Book

Solve x = 0 x 2 = -4 x = √(-4) In the real number system, there isn’t a number we can square to get -4. Imaginary numbers: Don’t think of them as “not real” Mathematicians chose this term for the square root of a negative number after they thought all real numbers were identified-(thought no real life application)

Imaginary Numbers

The square root of negative numbers Examples:

*For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead. Example:

Complex Numbers A complex number has a real part & an imaginary part.A complex number has a real part & an imaginary part. Standard form is:Standard form is: Real part Imaginary part Example: 5+4i

i Anytime you have √-1, you replace it with iAnytime you have √-1, you replace it with i √-16√-16 √16 * √-1√16 * √-1 4 * i4 * i 4i4i

How do we write the square root of a negative number? √-1 is called i or an imaginary unit—it is a way to describe the square root of a negative number√-1 is called i or an imaginary unit—it is a way to describe the square root of a negative number (√-1 ) 2(√-1 ) 2 √-1 * √-1√-1 * √-1 Therefore, i 2 = -1.Therefore, i 2 = -1. i = √-1 i 2 = -1i = √-1 i 2 = -1 i 3 = (√-1 ) 3 = -ii 3 = (√-1 ) 3 = -i i 4 = (√-1 ) 4 = -1*-1 = 1i 4 = (√-1 ) 4 = -1*-1 = 1

Write the complex number in standard form. 1. √-12. √-25 i5i 3. √-84. √-32 2i √2 4i √2 2i √2 4i √2

Complex Numbers (a + bi) real (a) + imaginary (bi) Real Numbers Just a (a + 0i) -1½ pi√3 Imaginary Numbers (a + bi, b ≠ 0) 2 + 3i5-5i Pure Imaginary Numbers (0 + bi, b ≠ 0, no a) -4i5i

Write the complex number in standard form √ √ i7-3i√3

With a partner, do p. 3 in M2 #’s 1-10