document.write( "Question 1170559: Write the following complex number in polar form: - 5+12i \n" ); document.write( "
Algebra.Com's Answer #795520 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
your equation is:
\n" ); document.write( "z = 5 + 12i
\n" ); document.write( "5 is the real term which forms the horizontal leg of the right triangle formed.
\n" ); document.write( "12i is the imaginary term where 12 forms the vertical leg of the right triangle formed.
\n" ); document.write( "the hypotenuse is called r.
\n" ); document.write( "r = sqrt(5^2 + 12^2) = sqrt(169) = 13
\n" ); document.write( "theta is the reference angle formed whose vertex is at the origin.
\n" ); document.write( "tan(theta) = 12/5
\n" ); document.write( "theta = arctan(12/5) = 67.38013505.
\n" ); document.write( "that's the reference angle which is the equivalent angle in the first quadrant.
\n" ); document.write( "the real part is on the x-axis.
\n" ); document.write( "the imaginary part is parallel to the y-axis.
\n" ); document.write( "because the real part is negative and the imaginary part is positive, the angle is in the second quadrant.
\n" ); document.write( "the equivalent angle in the second quadrant is 180 minus 67.38013505 = 112.6198649 degrees.\r
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\n" ); document.write( "\n" ); document.write( "the equation, in polar form is:
\n" ); document.write( "z = r * (cos(theta) + i * sin(theta))
\n" ); document.write( "that becomes:
\n" ); document.write( "z = 13 * (cos(112.6198649) + i * sin(112.6198649)\r
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\n" ); document.write( "\n" ); document.write( "that should be your solution.
\n" ); document.write( "you can convert it back to rectangular form by simplifying the equation to get:
\n" ); document.write( "z = 13 * (cos(112.6198649) + i * sin(112.6198649) is equal to:
\n" ); document.write( "z = 13 * (-.3846153846 + i * .9230769231) whish is equal to:
\n" ); document.write( "z = -5 + i * 12) which is the same as:
\n" ); document.write( "z = -5 + 12i\r
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\n" ); document.write( "\n" ); document.write( "an online polar coordinate calculator shows the following:\r
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\n" ); document.write( "\n" ); document.write( "\r
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\n" ); document.write( "\n" ); document.write( "this calculator can be found at https://www.intmath.com/complex-numbers/convert-polar-rectangular-interactive.php \n" ); document.write( "
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