document.write( "Question 1196798: prove that √ 2/2 + √ 2/2i is a square root of i \n" ); document.write( "

Algebra.Com's Answer #829802 by ikleyn(52777) $\"\"$ $\"About$

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document.write( "The square of the modulus of this number,   + , is\r\n" );
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document.write( "     =  +  =  =  +  = 1.\r\n" );
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document.write( "So, the modulus itself is  r =  = 1.\r\n" );
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document.write( "The argument of this number, \"a\", satisfies \r\n" );
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document.write( "    tan(a) =  = 1.\r\n" );
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document.write( "So, the argument is  a =  = 45°.\r\n" );
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document.write( "Hence, the square of this number has the modulus  = 1 and the argument 2a =  = 90°.\r\n" );
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document.write( "It means that the square of the given number is the complex imaginary unit \"i\".\r\n" );
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