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8. Prove that two nonzero complex numbers z1 and Z2 have the same moduli if and only if there are complex numbers c1 and c2 such that Z1 = c1C2 and Z2 = c1c2. Suggestion: Note that (i≤ exp (101+0) exp (01-02) and [see Exercise 2(b)] 2 02 Ꮎ - = = exp(i01) exp(101+0) exp (i 01 - 02 ) = exp(102). i 2 2

8. Prove that two nonzero complex numbers z1 and Z2 have the same moduli if and only if there are complex numbers c1 and c2 such that Z1 = c1C2 and Z2 = c1c2. Suggestion: Note that (i≤ exp (101+0) exp (01-02) and [see Exercise 2(b)] 2 02 Ꮎ - = = exp(i01) exp(101+0) exp (i 01 - 02 ) = exp(102). i 2 2

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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN: 9781133382119

Author: Swokowski

Publisher: Cengage

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Transcribed Image Text:8. Prove that two nonzero complex numbers z1 and Z2 have the same moduli if and only if there are complex numbers c1 and c2 such that Z1 = c1C2 and Z2 = c1c2. Suggestion: Note that (i≤ exp (101+0) exp (01-02) and [see Exercise 2(b)] 2 02 Ꮎ - = = exp(i01) exp(101+0) exp (i 01 - 02 ) = exp(102). i 2 2

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