$\"\"$

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The multiplication of complex numbers $\"\"$ .

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Let $\"\"$

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(a)

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The trigonometric form is $\"\"$ .

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The complex number is $\"\"$ .

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Compare the complex number with a + ib.

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a = $\"\"$ and b = 1.

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The absolute value of $\"\"$ : $\"\"$ .

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$\"\"$

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a = $\"\"$ =1.73 > 0, so the angle is :

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$\"\"$

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The trigonometric form of $\"\"$ .

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$\"\"$

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The complex number is $\"\"$ .

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Compare the complex number with a + ib.

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a = 1 and b = 1.

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The absolute value of $\"\"$ :

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$\"\"$

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a = 1 > 0, so the angle is :

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$\"\"$

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The trigonometric form of $\"\"$ . $\"\"$

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(b)

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Let $\"\"$ and $\"\"$ , then

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The product of two complex numbers: $\"\"$ .

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Here, $\"\"$ and $\"\"$ .

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Product of two complex numbers $\"\"$ .

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$\"\"$

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$\"\"$

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The result is $\"\"$ .

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$\"\"$

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(c)

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To check the solution, converting the complex numbers into standard forms.

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$\"\"$

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$\"\"$

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Multiply the standard forms : $\"\"$ .

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$\"\"$

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$\"\"$ .

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The result is $\"\"$ . $\"\"$

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The trigonometric form result is $\"\"$ .

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$\"\"$

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Substitute the values : $\"\"$ .

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$\"\"$

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$\"\"$ .

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The two results are same.

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$\"\"$

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The result is $\"\"$ .