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How can you express the complex number z = 2 + 3i in the form z = r(cos x + i sinx)

First you want to draw the complez number on to an argand diagram, using which you will find the modulus and argument. This is how to do so: The modulus is to be obtained using pythagoras (which will be easi...
MB
Answered by Meghali B. • Maths tutor
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Find the first 3 terms and the sum to infinity of a geometric series with first term, 10 and common ratio 0.2

General form of a Geometric series: a + ar + ar^2 + ar^3 + ar^4 + … First three terms: 10 + 10 0.2 + 10 0.2^2 = 10 + 0.2 + 0.04Nth Term of a Geometric Series: ar^n-1 where there are n terms Proof of sum of t...
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Answered by Daniel W. • Maths tutor
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How do you prove the 1^2 +2^2+.....+n^2 = n/6 (n+1) (2n+1) by induction?

There are three simple steps to prove anything by induction. Step 1: When n=1 1 2 =1 then: 1/6 x 1x (1+1) x (2+1) =1x2x3/6 =1 Therefore it is true for n=1 Step 2: Assume it is true for n=k so, 1 2 + 2 2 +......
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Answered by Vaisaalii I. • Maths tutor
5095 Views

Express the following as a partial fraction: (4x^2+12x+9) / (x^2+3x+2) .

We first notice that the degree of the numerator is the same as the degree of the denominator so we have an improper fraction which we need to separate into an integer and a proper fraction before we can exp...
AP
Answered by Antonia P. • Maths tutor
5614 Views

How do I write the function 3cosθ+4sinθ in the form Rsin(θ + α), where R and α are positive constants?

Split it up into steps: Step 1: Use compound angle trigonometric formula to re-write Rsin(θ + α) Since generally sin(θ ± φ) = sinθcosφ ± cosθsinφ Rsin(θ + α) = R(sinθcosα + cosθsinα) = Rsinθcosα + Rcosθsinα ...
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Answered by Oliver G. • Maths tutor
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