7.5_bzat4e - Example 5 Find z if z 3(cos 45 sin 45 ). i = +...

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Section 7.5 Complex Numbers in Polar Form: DeMoive’s Theorem
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The Complex Plane
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Example Determine the absolute value of each of the following: a. z=2+4i b. z=1-6i c. z=7i
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Polar Form of a Complex Number
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Example Plot z=3-2i in the complex plane. Then write z in polar form. Imaginary Axis Real Axis
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Example 0 0 Write z = 2 (cos 300 + i sin300 ) in rectangular form. Imaginary Axis Real Axis
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Products and Quotients in Polar Form
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Example 0 0 1 2 1 0 0 2 Find the product z z if z 3 (cos45 sin 45 ), and z 2 (cos135 sin135 ). i i = + = +
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Example 0 0 2 1 1 0 0 2 z Find the quotient if z 3 (cos 45 sin 45 ), and z 2 (cos135 sin135 ). i z i = + = +
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Example 0 0 2 1 1 0 0 2 z Find the quotient if z 10 (cos 60 sin 60 ), and z 5 (cos150 sin150 ). i z i = - + - = +
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Powers of Complex Numbers in Polar Form
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Unformatted text preview: Example 5 Find z if z 3(cos 45 sin 45 ). i = + Example 3 Find z if z 2(cos60 sin 60 ). i = + Roots of Complex Numbers in Polar Form Example Find all 5th roots of 1=1 (cos 0 sin 0 ) i + 1 2 3 4 5 x y Example Find all 4th roots of -8+8i 3=16 (cos120 sin 120 ) i + 1 2 3 4 5 x y (a) (b) (c) (d) Write the complex number z=- 3 in polar form. i + 2(cos30 +i sin30 ) 2(cos150 +i sin150 ) 2(cos60 +i sin60 ) 2(cos210 +i sin210 ) z z z z = = = = (a) (b) (c) (d) Write z=2(cos 300 sin 300 ) in rectangular form. i + 1 2 1 3 2 1 3 2 3 z i z i z i z i = -=-= -=-...
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7.5_bzat4e - Example 5 Find z if z 3(cos 45 sin 45 ). i = +...

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