Explanation Given information: The complex numbers : z = 3 ( cos 130 ∘ + i sin 130 ∘ ) and w = 4 ( cos 270 ∘ + i sin 270 ∘ ) Explanation: Theorem: Product of two complex numbers If z 1 = r 1 ( cos θ 1 + i sin θ 1 ) and z 2 = r 2 ( cos θ 2 + i sin θ 2 ) be two complex numbers. Then, z 1 z 2 = r 1 r 2 [ cos ( θ 1 + θ 2 ) + i sin ( θ 1 + θ 2 ) ] By using the theorem of product of two complex numbers, z w = [ 3 ( cos 130 ∘ + i sin 130 ∘ ) ] [ 4 ( cos 270 ∘ + i sin 270 ∘ ) ] ⇒ ( 3 ⋅ 4 ) [ cos ( 130 ∘ + 270 ∘ ) + i sin ( 130 ∘ + 270 ∘ ) ] ⇒ 12 ( cos 400 ∘ + i sin 400 ∘ ) Then, cos ( 400 ∘ ) = cos ( 400 ∘ − 360 ∘ ) = cos ( 40 ∘ ) and sin ( 400 ∘ ) = sin ( 400 ∘ − 360 ∘ ) = sin ( 40 ∘ ) Since the argument must lie between 0 0 and 360 0 ⇒ 12 ( cos 40 ∘ + i sin 40 ∘ ) Therefore, z w = 12 ( cos 40 ∘ + i sin 40 ∘ ) Quotient theorem of two complex numbers: If z 1 = r 1 ( cos θ 1 + i sin θ 1 ) and z 2 = r 2 ( cos θ 2 + i sin θ 2 ) be two complex numbers

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Author: Michael Sullivan

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Chapter 9.3, Problem 37AYU

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The product zw and quotient zw in polar form, where z=3(cos 130∘+ i sin 130∘) and w=4(cos 270∘+ i sin 270∘)

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Chapter 9.3, Problem 36AYU

Chapter 9.3, Problem 38AYU

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The product z w and quotient z w in polar form, where z = 3 ( cos 130 ∘ + i sin 130 ∘ ) and w = 4 ( cos 270 ∘ + i sin 270 ∘ )

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The product zw and quotient zw in polar form, where z=3(cos 130∘+ i sin 130∘) and w=4(cos 270∘+ i sin 270∘)

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