Complex Numbers
Complex Numbers Worksheet
Complex Numbers
1. Rewrite the following as a single complex number in the form 𝑎 + 𝑖𝑏 where 𝑎 and 𝑏 are integers.
a) √−4
b) √−25 + √1
c) 2√16 − 5√−9
2. Write the following as a single complex number.
a) 𝑖 3
b) (4𝑖)2
c) (5 + 2𝑖) + 3(1 − 2𝑖)
d) (6 + 𝑖)(2 − 3𝑖)
e) (2 + 𝑖)2
f) (3 + 𝑖)(3 − 𝑖)
Complex Conjugates
3. Find the complex conjugate of the following.
a) 5 + 2𝑖
b) 3 − 7𝑖
c) 4𝑖 − 6
d) 3(6 + 2𝑖)
Solving Quadratics
4. By completing the square or otherwise, solve the following quadratic equations (solutions are
complex numbers).
a) 𝑥 2 + 9
b) 𝑥 2 + 4𝑥 + 8
c) 𝑥 2 + 2𝑖𝑥 + 3
d) 𝑥 2 + 4𝑖𝑥 + 3
e) 3𝑥 2 − 6𝑖𝑥 + 9
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