To prove: x + y i satisfies the equation z 2 = a + b i , where x = b 2 y and y = ± a 2 + b 2 − a 2 .

Question

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Answer 1

Question

Chapter 7.2, Problem 21E

(a)

To determine

To prove: x+yi satisfies the equation z2=a+bi, where x=b2y and y=±a2+b2 −a2.

(b)

(i)

To determine

Two square roots of 3−4i.

(ii)

To determine

Two square roots of 4+3i.

(iii)

To determine

Two square roots of 5+12i.

(iv)

To determine

Two square roots of −12+5i.

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Assume {u1, U2, us} spans R³. Select the best statement. A. {U1, U2, us, u4} spans R³ unless u is the zero vector. B. {U1, U2, us, u4} always spans R³. C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set. D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³. OE. {U1, U2, 3, 4} never spans R³. F. none of the above

Assume {u1, U2, 13, 14} spans R³. Select the best statement. A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set. B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector. C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set. D. {U1, U2, us} always spans R³. E. {U1, U2, u3} may, but does not have to, span R³. F. none of the above

Answer 2

Question

Chapter 7.2, Problem 21E

(a)

To determine

To prove: x+yi satisfies the equation z2=a+bi, where x=b2y and y=±a2+b2 −a2.

(b)

(i)

To determine

Two square roots of 3−4i.

(ii)

To determine

Two square roots of 4+3i.

(iii)

To determine

Two square roots of 5+12i.

(iv)

To determine

Two square roots of −12+5i.

Expert Solution & Answer

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Answer 3

Question

Chapter 7.2, Problem 21E

(a)

To determine

To prove: x+yi satisfies the equation z2=a+bi, where x=b2y and y=±a2+b2 −a2.

(b)

(i)

To determine

Two square roots of 3−4i.

(ii)

To determine

Two square roots of 4+3i.

(iii)

To determine

Two square roots of 5+12i.

(iv)

To determine

Two square roots of −12+5i.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 7.2, Problem 21E

(a)

To determine

To prove: x+yi satisfies the equation z2=a+bi, where x=b2y and y=±a2+b2 −a2.

(b)

(i)

To determine

Two square roots of 3−4i.

(ii)

To determine

Two square roots of 4+3i.

(iii)

To determine

Two square roots of 5+12i.

(iv)

To determine

Two square roots of −12+5i.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 7.2, Problem 21E

(a)

To determine

To prove: x+yi satisfies the equation z2=a+bi, where x=b2y and y=±a2+b2 −a2.

(b)

(i)

To determine

Two square roots of 3−4i.

(ii)

To determine

Two square roots of 4+3i.

(iii)

To determine

Two square roots of 5+12i.

(iv)

To determine

Two square roots of −12+5i.

Answer 6

Chapter 7.2, Problem 21E

(a)

To determine

To prove: x+yi satisfies the equation z2=a+bi, where x=b2y and y=±a2+b2 −a2.

Answer 7

Chapter 7.2, Problem 21E

(a)

To determine

To prove: x+yi satisfies the equation z2=a+bi, where x=b2y and y=±a2+b2 −a2.

Answer 8

(b)

(i)

To determine

Two square roots of 3−4i.

Answer 9

(b)

(i)

To determine

Two square roots of 3−4i.

Answer 10

(ii)

To determine

Two square roots of 4+3i.

Answer 11

(ii)

To determine

Two square roots of 4+3i.

Answer 12

(iii)

To determine

Two square roots of 5+12i.

Answer 13

(iii)

To determine

Two square roots of 5+12i.

Answer 14

(iv)

To determine

Two square roots of −12+5i.

Answer 15

(iv)

To determine

Two square roots of −12+5i.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

To prove: x + y i satisfies the equation z 2 = a + b i , where x = b 2 y and y = ± a 2 + b 2 − a 2 .

Solution Summary: The author explains how x+yi satisfies the equation z2=a+bi.

Videos

To prove: x+yi satisfies the equation z2=a+bi, where x=b2y and y=±a2+b2 −a2.

Two square roots of 3−4i.

Two square roots of 4+3i.

Two square roots of 5+12i.

Two square roots of −12+5i.

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Chapter 7 Solutions