Imaginary numbers, complex numbers, quadratic formula, finding the root, etc.

kill me bro

What does √-49 equal?

7𝒾

What does √-16 equal?

4𝒾

What does √-20 equal? (simplest radical form)

2𝒾√5

What does √-3 equal? (simplest radical form)

𝒾√3

What does 3√-50 equal? (simplest radical form)

15𝒾√2

Multiply

(5+𝒾)(3-𝒾)

16-2𝒾

What does 𝒾⁰ equal?

1

What does 𝒾¹ equal?

𝒾

What does 𝒾² equal?

-1

Explanation: √-1×√-1=-1

What does 𝒾³ equal?

-𝒾

What does 𝒾⁴ equal?

1

What does 𝒾⁵ equal?

𝒾

What does 𝒾⁶ equal?

-1

What does 𝒾⁷ equal?

-𝒾

Simplify 7√(20x¹⁵)

14x⁷√5x

Add 3√27 + 5√12

19√3

Multiply

(6+√3)²

39+12√3

Multiply

(8+√7)(8-√7)

57

Multiply

(4+2𝒾)(3-7𝒾)

26-22𝒾

Subtract

(10+2𝒾) - (7-4𝒾)

3+6𝒾

Multiply

(2+5𝒾)(3-7𝒾)

41+𝒾

Multiply

(5+2𝒾)²

21+20𝒾

Multiply

(7+√3)(7-√3)

46

Find the solution set

x²-12=4x

{6, -2}

Solve

x²-6x+1=0

x=3±2√2

Solve

x²+6x+13=0

x=-3±2𝒾

Solve

x²-8x+17=0

x=4±𝒾

Solve

x²+4x-3=0

x=-2±√7

Solve

x²-6x+58=0

x=3±7𝒾

Solve

x²+4x+1=0

x=-2±√3

Solve using completing the square. 

x²-6x+58=0

x=3±7𝒾

Solve using completing the square. 

x²+4x+1=0

x=-2±√3

Solve using completing the square. 

x²-12x+37=0

x=6±𝒾

Solve

x²-8x+17=0

x=4±𝒾

Solve using completing the square. 

x²+6x-1=0

x=-3±√10

Find the solution set of the higher degree equation.

x³+3x²-9x-27=0

{-3,3}

Find the solution set of the higher degree equation.

6x³-8x²-8x=0

{0, -2/3, 2}

Find the solution set of the higher degree equation.

12x³+20x²-8x=0

{0, 1/3, -2}

Find the solution set of the higher degree equation.

x³+8=0

{-2, 1±𝒾√3}

4+√(1-3x)=12

{-21}

x=√(3x+10)

{5}

x=√4x+5

{5}

x=1+√(x+11)

{5}

b=3+√(3b+11)

{5, 4}

Factor

b³-343

(b+7)(b²+7b+49)

What is the SOAP formula?

(a+b)(a²-ab+b²)

(a-b)(a²+ab+b²)

Factor

8x³-125

(2x-5)(4x²+10+25)

Factor

x³+125

(x+5)(x²-5x+25)

Factor

a³-64

(a-4)(a²+4a+16)

Factor

7√(45x¹¹)

21x⁵√(5x)

Factor

3√(50y¹⁵)

15y⁷√(2y)

Factor 

7∛(24x¹¹)

14x³∛3x²

Factor

4∛(54x⁷)

12x²∛2x

Factor

5∛(40a¹⁷)

10a⁵∛5a²

Solve

√(2x-3)+7=12

x=14

Solve

x=1+√(15-7x)

{2}

Solve

x³-5x²-6x+30=0

{±√6,5}

Solve

2x^3-6x²-20x=0

{5, -2, 0}

Solve

x²+6x+2=0

x=-3±√7

Solve

x²-6x+10=0

x=3±𝒾

Factor

x³+27

(x+3)(x²-3x+9)

Solve

√(4-x)=x+8

{5}

Find the roots of the equation

x²-4x=-13

2±3𝒾

Solve

√(3(x+6))=x

{6}