Lemma

Complex Numbers · Chapter 1 of 6

Arithmetic of ℂ

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Multiply complex numbersEasy · 42 million variations

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#TitleDifficultySourceTags
124The cycle of iEasyLemmaPowers of iPeriodicity
125Dividing by a complex numberEasyLemmaConjugate
126A modulus without multiplyingEasyLemmaModulusMultiplicativity
269Adding complex numbersEasyLemmaArithmetic of ℂ
270Multiplying complex numbersEasyLemmaArithmetic of ℂ
271Squaring a complex numberEasyLemmaArithmetic of ℂ
272A quotientEasyLemmaArithmetic of ℂ
273A Pythagorean modulusEasyLemmaArithmetic of ℂ
274One over iEasyLemmaArithmetic of ℂ
276A hundred powers of iEasyLemmaArithmetic of ℂ
1181Complex Fraction SimplificationEasyHall & KnightComplex numbersRationalization
1185Power of Imaginary UnitEasyHall & KnightPowers of iModular arithmetic
1187Square Root of Complex NumberEasyHall & Knightsquare root of complex numberimaginary numbers
1188Square Root of Complex NumberEasyHall & Knightsquare root of complex numberimaginary numbers
1190Square Root of Pure Imaginary NumberEasyHall & Knightsquare root of complex numberimaginary numbers
1193Complex divisionEasyHall & Knightcomplex numbersdivision
1194Complex division with radicalsEasyHall & Knightcomplex numbersradicals
1195Simplifying a quotient of binomialsEasyHall & Knightcomplex numberspowers of i
1196Complex fraction with squared numeratorEasyHall & Knightcomplex numbersexpansion

From open sources

157

Showing everything, including problems with no answer to check, a missing figure, or a near-copy elsewhere. Show only complete problems

#TitleDifficulty
100180Simplify a radical expression using the Product Property.Easy
100189Complex Numbers · Example 2Easy
100201Expressing an Imaginary Number in Standard FormEasy
100205Adding and Subtracting Complex NumbersEasy
100207Multiplying a Complex Number by a Real NumberEasy
100209Multiplying a Complex Number by a Complex NumberEasy
100211Finding Complex ConjugatesEasy
100213Dividing Complex NumbersEasy
100214Simplifying Powers of iEasy
100216Complex Numbers · Exercise 20Easy
100218Complex Numbers · Exercise 22Easy
107124Adding Complex NumbersEasy
107128Substituting an Imaginary Number in a Rational FunctionEasy
107130Complex Numbers · Exercise 3Easy
125718Use the Complex Number System · Example 1Easy
125721Use the Complex Number System · Example 2Easy
125724Use the Complex Number System · Example 3Easy
125727Use the Complex Number System · Example 4Easy
125730Use the Complex Number System · Example 5Easy
125736Use the Complex Number System · Example 7Easy
125739Use the Complex Number System · Example 8Easy
125742Use the Complex Number System · Example 9Easy
125751Use the Complex Number System · Example 12Easy
125754Use the Complex Number System · Example 13Easy
100202Complex Numbers · Try It 1Easy
100206Complex Numbers · Try It 3Easy
100208Complex Numbers · Try It 4Easy
100210Complex Numbers · Try It 5Easy
100212Complex Numbers · Try It 6Easy
100215Complex Numbers · Try It 7Easy
107125Complex Numbers · Try It 4Easy
107127Complex Numbers · Try It 6Easy
107129Complex Numbers · Try It 7Easy
125719Use the Complex Number System · Try It 1Easy
125720Use the Complex Number System · Try It 2Easy
125722Use the Complex Number System · Try It 3Easy
125723Use the Complex Number System · Try It 4Easy
125725Use the Complex Number System · Try It 5Easy
125726Use the Complex Number System · Try It 6Easy
125728Use the Complex Number System · Try It 7Easy
125729Use the Complex Number System · Try It 8Easy
125731Use the Complex Number System · Try It 9Easy
125732Use the Complex Number System · Try It 10Easy
125734Use the Complex Number System · Try It 11Easy
125735Use the Complex Number System · Try It 12Easy
125737Use the Complex Number System · Try It 13Easy
125738Use the Complex Number System · Try It 14Easy
125740Use the Complex Number System · Try It 15Easy
125741Use the Complex Number System · Try It 16Easy
125743Use the Complex Number System · Try It 17Easy
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