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junior college 1 | H1 Maths
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Anyone able to solve for Z regarding this complex numbers problem
Date Posted: 4 years ago
Views: 305
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done
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clear
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The number is weird looking though.
Date Posted:
4 years ago
Thanks should be correct despite the weird answer...i got the same answer too with a diff method
z² = 96 - 168i
Express in exponential form.
r = √(96² + 168²)
r = √37440
tan θ = -168/96 = -7/4
θ = tan-¹ (-7/4) ≈ -1.052 rad
z² lies in the third quadrant so arg (z²) = -1.052 rad
so z² = √37440 e^(-1.052i)
= √37440 e^(-1.052 + 2kπ)i, k ∈ Z
z = √(√37440 e^(-1.052+ 2kπ)i)
z = ⁴√37440 e^((-1.052 + 2kπ)i/2) , k = 0, 1
z = ⁴√37440 e^(-1.052i/2) , ⁴√37440 e^((-1.052 + 2π)i/2)
z ≈ -6.98402i + 12.0299, 6.98402i -12.0299
Express in exponential form.
r = √(96² + 168²)
r = √37440
tan θ = -168/96 = -7/4
θ = tan-¹ (-7/4) ≈ -1.052 rad
z² lies in the third quadrant so arg (z²) = -1.052 rad
so z² = √37440 e^(-1.052i)
= √37440 e^(-1.052 + 2kπ)i, k ∈ Z
z = √(√37440 e^(-1.052+ 2kπ)i)
z = ⁴√37440 e^((-1.052 + 2kπ)i/2) , k = 0, 1
z = ⁴√37440 e^(-1.052i/2) , ⁴√37440 e^((-1.052 + 2π)i/2)
z ≈ -6.98402i + 12.0299, 6.98402i -12.0299
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