Square root of a complex number (HSC SSCE Mathematics Extension 2): Flashcards
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What is a complex number?
What is a complex number?
A number in the form z = a + bi, with a, b real.
Why are complex numbers important in advanced maths?
Why are complex numbers important in advanced maths?
They help solve equations without real solutions.
What is the general form of a complex number?
What is the general form of a complex number?
z = a + bi, with a and b real numbers.
How do you find the square root of z = a + bi?
How do you find the square root of z = a + bi?
Assume √z = x + iy; solve (x + iy)^2 = a + bi.
Where do complex roots appear on an Argand diagram?
Where do complex roots appear on an Argand diagram?
Symmetrically about the real axis.
What role do real and imaginary parts play in the method?
What role do real and imaginary parts play in the method?
They are separated into equations to solve for x and y.
What is a complex number?
What is a complex number?
z = a + bi with a,b real and i^2 = -1
Real and imaginary parts from (x+iy)^2?
Real and imaginary parts from (x+iy)^2?
x^2 - y^2 = a and 2xy = b
How to verify a computed square root?
How to verify a computed square root?
Substitute x,y into (x+iy)^2 and check it equals z
How to find sqrt(a+bi)?
How to find sqrt(a+bi)?
Assume x+iy; solve x^2 - y^2 = a and 2xy = b