document.write( "Question 1201677: PLEASE do GIVE CoRRECT AnSwers\r
\n" ); document.write( "\n" ); document.write( "1. Convert the rectangular form of the complex number 2-2i
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\n" ); document.write( "\n" ); document.write( "2. Find all cube roots of the complex number 64(cos(219 degree) + i sin (219 degree)). Leave answers in polar form and show all work. \n" ); document.write( "

Algebra.Com's Answer #836162 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The number 2-2i is located in 4th quadrant, QIV.\r\n" );
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document.write( "Its modulus is   =  =  = .\r\n" );
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document.write( "Its argument is -45°  or  360°-45° = 315°.   \r\n" );
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document.write( "(You may use any of these two values, -45° or 315°, they both represent the correct arguments).\r\n" );
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document.write( "So, the polar form of a complex number 2-2i is\r\n" );
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document.write( "    2 - 2i = .\r\n" );
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document.write( "It is the same as to say that the polar form of a complex number 2-2i is\r\n" );
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document.write( "    2 - 2i = .\r\n" );
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document.write( "In \"cis\"-form,  it is the same as\r\n" );
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document.write( "    2 - 2i =  = .\r\n" );
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document.write( "The modulus is ;  the argument  is -45° or 315°  or any other number of degrees \r\n" );
document.write( "which differs by a multiple of 360° from -45° or from 315°.\r\n" );
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document.write( "To make the argument unique, sometimes the conception of a PRINCIPAL ARGUMENT is used and the principal argument is taken: \r\n" );
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document.write( "    it is the value of an argument in the range [0°,360°),\r\n" );
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document.write( "    i.e. 315° in this problem.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On complex numbers, see introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - Complex numbers and arithmetical operations on them\r
\n" ); document.write( "\n" ); document.write( "    - Complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Addition and subtraction of complex numbers in complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Multiplication and division of complex numbers in complex plane\r
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\n" ); document.write( "\n" ); document.write( "    - Solved problems on taking roots of complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic operations on complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Solved problem on taking square root of complex number\r
\n" ); document.write( "\n" ); document.write( "    - Solving polynomial equations in complex domain \r
\n" ); document.write( "\n" ); document.write( "    - Miscellaneous problems on complex numbers\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook on ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Complex numbers\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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