Complex Numbers — Drills
Complex Numbers has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 6 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Exponent — How many times the base is used as a factor. In 53 the exponent is 3.
- Binomial — A polynomial with two terms.
- Roots — The x values where y = 0.
- Discriminant — b2 - 4ac. Its sign counts the real solutions.
- Remainder — What is left when the divisor no longer fits. Always lower degree than the divisor.
- Conjugate — a - bi is the conjugate of a + bi. Multiplying them clears the i entirely.
Powers
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify i35.
Worked answer
-i
35 = 4(8) + 3
i3 = -i
Problem 2
Simplify i48.
Worked answer
1
48 = 4(12) + 0
i0 = 1
Adding
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify (2+7i)+(5-2i).
Worked answer
7+5i
2+5=7
7i-2i=5i
Problem 2
Simplify (5+6i)+(1-9i).
Worked answer
6-3i
5+1=6
6i-9i=-3i
Multiplying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Expand (4+4i)(6-3i).
Worked answer
36+12i
24 - 12i + 24i - 12i2
-12i2 = +12
36+12i
Problem 2
Expand (5+3i)(3-2i).
Worked answer
21-1i
15 - 10i + 9i - 6i2
-6i2 = +6
21-1i
Conjugate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Give the conjugate of 2+5i.
Worked answer
2-5i
The real part is unchanged
2-5i
Problem 2
Give the conjugate of 4-4i.
Worked answer
4+4i
The real part is unchanged
4+4i
Roots
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write √-81 in terms of i.
Worked answer
9i
√-81=√81√-1
=9i
Problem 2
Write √-9 in terms of i.
Worked answer
3i
√-9=√9√-1
=3i
Norm
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Expand (7+5i)(7-5i).
Worked answer
74
49 - 25i2
=49+25=74
Problem 2
Expand (1+4i)(1-4i).
Worked answer
17
1 - 16i2
=1+16=17