Input the real and imaginary parts and get the result in seconds.
The modulus (or absolute value) of a complex number represents its distance from the origin in the complex plane. For a complex number \( z = a + bi \): \( |z| = \sqrt{a^2 + b^2} \) Where: \( a \) is the real part of the complex number, \( b \) is the imaginary part of the complex number.
Solution:
\( |3 + 4i| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \)
Result: The modulus of \( 3 + 4i \) is \( 5 \).
Solution:
\( |1 - 2i| = \sqrt{1^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.24 \)
Result: The modulus of \( 1 - 2i \) is approximately \( 2.24 \).
Solution:
\( |-3 + 4i| = \sqrt{(-3)^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \)
Result: The modulus of \( -3 + 4i \) is \( 5 \).