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Level 357

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in an equation

square roots only produce negative and positive numbers when

check for exteraneous

if both sides are squared (or raised to a power divisible by two)

it's positive and negative _______

when you take the square root of both sides of the equation

i=

√-1

SIMPLIFY FIRST

when dealing with imaginary numbers, always

a+bi

complex numbers: formula

a

what is the real part of a+bi

bi

what is the imaginary part of a+bi

6

real part of: 6+7i

0

real part of: 12i

1/2

Cos 60

0

real part of: i/2

2

real part of: 8+3i/4

7i

imaginary part of: 6+7i

12i

imaginary part of: 12i

0 (0i)

imaginary part of: 1/2

i/2 (1/2i)

imaginary part of: i/2

3/2i

imaginary part of: 8+3i/2

a-bi

the complex conjugate of a+bi is

-8

8i^2 simplifies to

a real number

when you multiply a complex number by it's conjugate, you get

denominator of a fraction

you never want to have imaginary numbers on the

when you have imaginary numbers on the denominator of a fraction, you should

multiply the fraction by that thing (or if it's a complex number, by it's conjugate)

f(x)=(x-(2+i))(x-(2-i)) which simplifies to f(x)=x^2-4x+5

when given the roots: 2+i and 2-i, you write the function

another way to get a quadratic expression (a simplified function) when given roots with imaginary numbers

the roots can also be used to get you a, b, and c (which you plug into the quadratic expression to get a simplified function)

-b/a

the sum of the roots (addition) is

c/a

the product of the roots (multiplication) is

can be divided by two

if a number is even it

k

you can tell if a number is divisible by three if

you can tell if a number is divisible by 4 if

the last two numbers of the number are divisible by four (like 1240847903758264)

i^1=i

powers of i

i^1=

i

i^2=

-1

i^3=

-i

i^4=

1

the quadratic expresion

when trying to find complex roots, one can always use

the quadratic expression

-b +- √b^2 -4ac / 2a

equivalent complex numbers

set 'a's of a+bi equal and 'bi's from a+bi in an equation equal

all numbers/variables with 'i' in them

what do you set equal to 'bi' in equivalent complex numbers

all numbers/variables without 'i' in them

what do you set equal to 'a' in equivalent complex numbers