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Is there an existing formula to raise a complex number to a power? That is, I want to compute $(1 + i)^N$. I basically want to write a function like so: def raiseComplexNumberToPower(float real, ...

Oct 22, 2017 · I have the complex number 3 + i 3 + i, and I am asked to get the complex number resulted by rotating the first one by π4 π 4. I got the polar form of the first one to get its angle (18.43° 18.43 °) but when I add π 4 π 4 to it and try to find its cartesian form, the result is different. Am I doing something wrong with the procedure? If so, what can I do?

The square root is not a well defined function on complex numbers. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number.

What are the steps in solving for the question: For i2 =– 1 i 2 = – 1, what is (4 + i)2 (4 + i) 2 The answer I was given was 15 + 8i 15 + 8 i but I'm unsure how this was the answer and what steps were taken to get there. Thank you.

Using this formula, you only need to know how to do exponentiation with real numbers, finding the angle of a complex number, finding ln (x), finding |x|, euler's formula, multiplication, division, addition and sometimes subtraction.

Dec 3, 2019 · Every complex number (except 0 0) has three cube roots. A quicker way to find these roots is to use the cube roots of unity, which can be written 1, ω,ω2 1, ω, ω 2 and multiply them successively by the root you've already got.

When you write your complex number as an e-power, your problem boils down to taking the Log of (1 + i) (1 + i). Now that is ln 2–√ + iπ 4 ln 2 + i π 4 and here it comes: + all multiples of 2iπ 2 i π.

Mar 18, 2016 · I've been pondering over this question since a very long time. If a complex number can be prime then which parts of the complex number needs to be prime for the whole complex number to be prime.

Aug 19, 2018 · Are z2 z 2 and |z|2 | z | 2 same? Where z z is a complex number. If imaginary part of z z is zero, then surely we can say they are both are same. What about if imaginary part of z z is non-zero?

Jan 24, 2013 · We can define the norm of a complex number in other ways, provided they satisfy the following properties Positive homogeneity Triangle inequality Zero norm iff zero vector We could define a 3 -norm where you sum up all the components cubed and take the cubic root. The infinite norm simply takes the maximum component's absolute value as the norm.