Lemma

Complex Numbers · Chapter 1 of 6

Arithmetic of ℂ

31 curated · 142 from open sources · 43 million generated

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31
#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
275An equation with a conjugateMediumLemmaArithmetic of ℂ
1182Algebraic Complex FractionMediumHall & KnightComplex numbersAlgebraic manipulation
1183Binomial Complex FractionsMediumHall & KnightComplex numbersRationalization
1184Cubic Difference Complex FractionMediumHall & KnightComplex numbersAlgebraic identities
1186Square of Sum of RadicalsMediumHall & KnightComplex numbersRadicals
1189Square Root of Complex NumberMediumHall & Knightsquare root of complex numbersurds
1191Square Root with ParameterMediumHall & Knightsquare root of complex numberalgebraic parameters
1192Square Root with Two ParametersMediumHall & Knightsquare root of complex numberalgebraic parameters
1197Algebraic complex fraction combinationMediumHall & Knightcomplex numbersalgebraic simplification
1222Evaluate polynomial at complex numberMediumHall & Knightcomplex substitutionpolynomial evaluation
1223Evaluate cubic at complex numberMediumHall & Knightcomplex substitutionpolynomial evaluation
1224Evaluate cubic with parameterMediumHall & Knightcomplex numbersalgebraic manipulation

From open sources

142

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#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
100220Complex Numbers · Exercise 24Medium
100222Complex Numbers · Exercise 26Medium
100224Complex Numbers · Exercise 28Medium
100229Complex Numbers · Exercise 34Medium
100231Complex Numbers · Exercise 36Medium
100233Complex Numbers · Exercise 38Medium
100235Complex Numbers · Exercise 40Medium
100237Complex Numbers · Exercise 42Medium
100238Complex Numbers · Exercise 44Medium
100240Complex Numbers · Exercise 46Medium
100242Complex Numbers · Exercise 48Medium
100244Complex Numbers · Exercise 50Medium
100246Complex Numbers · Exercise 52Medium
100248Complex Numbers · Exercise 54Medium
100250Complex Numbers · Exercise 56Medium
100252Complex Numbers · Exercise 58Medium
100254Complex Numbers · Exercise 60Medium
100256Complex Numbers · Exercise 62Medium
100258Complex Numbers · Exercise 64Medium
100260Complex Numbers · Exercise 66Deep
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