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Can you express 3 + 4j in polar form?

First, let's imagine the point 3 + 4j as a point on an Argand diagram, with coordinates 3,4. The polar form of an imaginary number is in the form re^(jθ), where r is the modulus of the number (the distanc...

Answered by Walter T. • Further Mathematics tutor

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How do you prove by induction?

First you prove the case n=1 is true. Then you assume that n=k is true, then calculate what n=k+1 is. This should prove true, so that by induction, you have proved that the statement is true for all natur...

Answered by Praveenaa K. • Further Mathematics tutor

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How do I know I can multiply two matrices and if so, how do I do it?

Firstly you need to check if the matrices conform. Matrices are an array of elements within a pair of brackets, there are some number of columns, usually denoted m, and some number of rows, denoted n. The...

Answered by Mark D. • Further Mathematics tutor

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Find the general solution of: y'' + 4y' + 13y = sin(x)

First we find the auxilary equation by substituting y with m^0, y' with m^1 and y'' with m^2. We get m^2 + 4m + 13 and find the roots using the differential equation, m = (-4 +- (16-4x1x13)^0.5)/(2x1).

Answered by Tom T. • Further Mathematics tutor

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Write 1 + √3i in modulus-argument form

In order to understand this question we must define what modulus-argument form is. The modulus of a complex number is its distance from the origin (0,0) on the Argand Diagram. It is written as |z|. The ar...

Answered by Tom M. • Further Mathematics tutor

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