Question | Answer |
What is the square root of negative 36?
√-36 | √-36
= √36 x √-1
= 6 x i
= 6i |
How about the negative square root of negative 36?
-√-36 | -√-36
= -(√36 x √-1)
= -6 x i
= -6i |
Solve this equation
(7 + 2i) + (2 + 4i) | (7 + 2i) + (2 + 4i) = (7 + 2) + (2 + 4)i = 9 + 6i |
Now we’ll try the same problem with a negative i
(7 - 2i) + (2 + 4i) | (7 - 2i) + (2 + 4i) = (7 + 2) + (-2 + 4)i = 9 + 4i |
Subtraction is just as easy
(7 + 4i) - (2 + 2i) | (7 + 2i) - (2 + 4i) = (7 - 2) + (2 - 4)i = 5 - 2i |
Don’t be fooled if there isn’t a second real number
(7 + 2i) - (4i) | (7 + 2i) - (4i) = (7 - 0) + (- 4)i = 7 - 2i |
When multiplying complex numbers remember that the product rule for radicals doesn’t apply
√-36 x √-49 | √-36 x √-49 = 6i x 7i = 42i2 = 42(-1) = -42 |
Here’s another multiplication example
6i(2 - 7i) | 6i(2 - 7i) = 12i – 42i2 = 12i – 42(-1) = 12i + 42 = 42 + 12i |
Remember the FOIL method?
(2 - 7i)(4 + 3i) | (2 - 7i)(4 + 3i) = 8 + 6i - 28i – 21i2 = 8 – 22i - 21i2 = 8 – 22i - 21(-1) = 8 – 22i + 21 = 29 – 22i |
Conjugate is hard to say but we need it for division
2 + 4i / 3 – 6i | 2 + 4i / 3 – 6i = (2 + 4i x 3 + 6i) / (3 – 6i x 3 + 6i) = 6 + 12i + 12i + 24i2 / 9 + 18i – 18i – 36i2 = 6 + 24i + 24(-1) / 9 – 36(-1) = (-18 + 24i) / 45 = - 18/45 + 24i / 45 |