Difficulty
Calculator
Interactive test · 24 problems, easy → medium → hard. Powers of ⅈ, roots of negatives, add/subtract/multiply/divide, conjugates, and modulus.
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Easy Simplify: \(\sqrt{-9}\).
Answer: B — \(3i\)
Easy Simplify: \(i^{2}\).
Answer: D — \(-1\)
Easy Simplify: \(\sqrt{-25}\).
Answer: A — \(5i\)
Easy Simplify: \((3+2i)+(5+4i)\).
Answer: C — \(8+6i\)
Easy Simplify: \((7+5i)-(2+3i)\).
Answer: C — \(5+2i\)
Easy Simplify: \(i^{4}\).
Answer: D — \(1\)
Easy Write in terms of \(i\): \(\sqrt{-16}\).
Answer: B — \(4i\)
Medium Simplify: \(\sqrt{-12}\).
Answer: D — \(2i\sqrt{3}\)
Medium Simplify: \(i^{3}\).
Answer: C — \(-i\)
Medium Simplify: \(i^{7}\).
Answer: B — \(-i\)
Medium Simplify: \(3i \cdot 4i\).
Answer: D — \(-12\)
Medium Simplify: \(2i(3+i)\).
Answer: C — \(-2+6i\)
Medium Simplify: \((2+3i)(1+4i)\).
Answer: B — \(-10+11i\)
Medium What is the complex conjugate of \(5-2i\)?
Answer: D — \(5+2i\)
Medium Find the absolute value (modulus): \(|\,3+4i\,|\).
\(=\)Answer: \(5\)
Medium Simplify: \((3+2i)(3-2i)\).
\(=\)Answer: \(13\)
Medium Simplify: \(i^{20}\).
Answer: B — \(1\)
Hard Simplify: \(i^{50}\).
Answer: B — \(-1\)
Hard Simplify: \((4-i)^{2}\).
Answer: C — \(15-8i\)
Hard Write in standard form: \(\dfrac{1}{2+i}\).
Answer: A — \(\dfrac{2}{5}-\dfrac{1}{5}i\)
Hard Write in standard form: \(\dfrac{3+2i}{1-i}\).
Answer: A — \(\dfrac{1}{2}+\dfrac{5}{2}i\)
Hard Solve for \(x\): \(x^{2}=-49\).
Answer: C — \(x=\pm 7i\)
Hard Find the modulus: \(|\,-6+8i\,|\).
\(=\)Answer: \(10\)
Hard Simplify: \(\sqrt{-8}\cdot\sqrt{-2}\).
\(=\)Answer: \(-4\)