Let-sinh-1-a-bi-c-di-where-a-b-c-d-R-b-0-and-i-1-Find-each-of-c-and-d-in-terms-of-a-and-b-For-f-x-sinh-1-x-f-is-the-arc-hyperbolic-sine-function-

Tinku Tara June 3, 2023 Algebra 0 Comments

Question Number 4970 by Yozzii last updated on 28/Mar/16

Let sinh^(−1) (a+bi)=c+di where a,b,c,d∈R, b≠0 and i=(√(−1)). Find each of c and d in terms of a and b. For f: x∣→sinh^(−1) x, f is the arc,hyperbolic sine function.

$${Let}\:{sinh}^{−\mathrm{1}} \left({a}+{bi}\right)={c}+{di}\:{where}\:{a},{b},{c},{d}\in\mathbb{R}, \\ $$$${b}\neq\mathrm{0}\:{and}\:{i}=\sqrt{−\mathrm{1}}.\:{Find}\:{each}\:{of}\:{c}\:{and}\:{d}\:{in}\:{terms} \\ $$$${of}\:{a}\:{and}\:{b}.\:{For}\:{f}:\:{x}\mid\rightarrow{sinh}^{−\mathrm{1}} {x},\:{f}\:{is}\:{the}\: \\ $$$${arc},{hyperbolic}\:{sine}\:{function}. \\ $$

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Let-sinh-1-a-bi-c-di-where-a-b-c-d-R-b-0-and-i-1-Find-each-of-c-and-d-in-terms-of-a-and-b-For-f-x-sinh-1-x-f-is-the-arc-hyperbolic-sine-function-

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