Complex Number Kookiness 8

(√(x) + i√(x))2 = 2xi

This math trick is similar to "Complex Number Kookiness 6" since you get the same result; however, it's a completely different formula!

Examples:

(√(2) + i√(2))2 = 4i

(√(3) + i√(3))2 = 6i

(√(-4) + i√(-4))2 = (-2 + 2i)2 = -8i

(2i * i = -2 since i2 = -1; also, it's proper complex number form to put the real part on the left & the imaginary part on the right.)

(√(1) + i√(1))2 = (1 + i)2 = 2i

(the number 1 is its own square root! Don't forget it!)

(√(0) + i√(0))2 = (0 + 0i)2 = 0i = 0

(That goes double for the number zero(0)! Plus, any number multiplied by zero is still zero!)

This math trick works with all numbers; however, if you pick an imaginary or complex number for x, then... Well, look at the examples below to find out:

(√(i) + i√(i))2 = -2

(√(-i) + i√(-i))2 = 2

(√(1 + i) + i√(1 + i))2 = -2 + 2i

(√(1 - i) + i√(1 - i))2 = 2 + 2i

2xi will be equal to a real number or a complex number if x is a non-real number! You'll get a real number if x is a pure imaginary number! If x is equal to a negative imaginary number, then 2xi will be equal to a positive real number! If x is equal to a positive imaginary number, then 2xi will be equal to a negative real number!

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© Derek Cumberbatch