Radical Expressions and Imaginary Numbers

Evaluating

100

sqrt(x)+5=7

4

200

sqrt(x-5)=2

9

300

root(3)(x)+5=10

125

400

root(3)(x-7)=2

15

500

(x-5)^(1/3)=4

69

Rational Exponents

100

49^(1/2)

7

200

64^(3/2)

512

300

16^(3/4)

8

400

(x^8)^(1/2)

x^4

500

(x^15)^(2/5)

x^6

Imaginary and Complex Numbers

100

sqrt(-16)

4i

200

sqrt(-81)

9i

300

root(4)(-16)

2i

400

sqrt(25)+sqrt(-100)

5+10i

500

root(3)(-64)+sqrt(-64)

-4+8i

Complex Numbers Operations

100

(6+4i)+(3+9i)

9+13i

200

(7-2i)+(5+8i)

12+6i

300

(10+5i)-(3+2i)

7+3i

400

(4+2i)(5+3i)

14+22i

500

(8+i)(6+4i)

44+38i

Real or Fake?

100

Are the solutions real or non-real?

x²-3x+5

non-real

200

Are the solutions real or non-real?

x²+3x+1

Real!

300

Are the solutions real or non-real?

2x²-7x+8

Non-real!

400

What's the next step using imaginary numbers?

(x-5)²=-16

square root both sides.

x=5+4i

500

What's the next step using imaginary numbers?

x=(-5+-sqrt(100-104))/10

x=(-5+-2i)/10