i is an imaginary number such that i^2 = -1. A complex number is written in the form a + bi, where a is the real part and b is the imaginary part. To solve an equation involving complex numbers, one sets the real and imaginary parts equal to find the values of the variables.

1. Not a real number
i is an imaginary
number
i2 = 1

2. Simplify 4
4
Simplify: 16
25 x4 x
=

3. Simplify
=6
Simplify
=

4. Simplify
6
12
4(3)
=

5. Simplify
-1even = 1
-1odd = -1

6. 38 19
Simplify
19
-1even = 1
-1odd = -1

7. A complex number is written in the form:
a + bi
Real part Imaginary part
3 + 8i 0 – 6i
4 – 12i

8. Simplify
= 4 – 6i – 3 + 7i
= 4 – 3 – 6i + 7i
=1+i

9. Find the values of x and y that make the
equation true.
Real parts Imaginary parts
yi = -3i
Answer:

10. Multiply: (3 + 2i)(4 – 3i)
= 12 – 9i + 8i – 6i2
= 12 – i – 6(-1)
= 12 – i + 6
= 18 – i

11. Simplify

12. Simplify

13. Solve
5 5
2nd degree equation
two solutions
y2

14. Solve
2x2 = -50
2 2
x2 = -25
x2 =  -25
x =  5i