Great thanks.andrewkirk said:That is correct.
squenshl said:Great thanks.
I get ##a=b= \pm\sqrt{10}## so ##w## follows.
Ray Vickson said:No, ##a = b = -\sqrt{10}## would not be correct; only the ##+\sqrt{10}## answer applies.
I do.RPinPA said:Do you understand Ray's point? What is ##\arg(w)## if ##a = b## and both are negative?
A complex number is a number that contains both a real and an imaginary part. It is expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit equal to the square root of -1.
The modulus of a complex number is the distance of the number from the origin on the complex plane. It is calculated by taking the square root of the sum of the squares of the real and imaginary parts.
The argument of a complex number is the angle between the positive real axis and the line connecting the number to the origin on the complex plane. It is measured in radians or degrees and can be calculated using trigonometric functions.
To find a complex number given its argument and modulus, you can use the polar form of complex numbers. The real part of the number is equal to the modulus multiplied by the cosine of the argument, and the imaginary part is equal to the modulus multiplied by the sine of the argument.
Yes, a complex number can have multiple values for its argument and modulus, as there are an infinite number of ways to represent the same number on the complex plane. These different representations are known as equivalent forms of the complex number.