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# Given the following complex number, find the following.

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Given the following complex number, find the following.

3√2 + 6i^87

a) Simplify the complex number to not include any large exponents.

b) Find the modulus.

any pointers would be appreicated

May 12, 2020

#1
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I will assume this is  6 (i^87)

rememeber this:             i^2 = -1         i^3 = -i           i^4 = 1

6 (i^87)    =  6  (i^4)21 * i^3     = 6* 1* -i  =   -6i

3 sqrt 2  - 6i

modulus = sqrt of both parts squared and added

sqrt(  (3 sqrt2)^2  +  (-6i)^2)

sqrt( 18 + -36(-1) ) =  sqrt 54

May 12, 2020
edited by ElectricPavlov  May 13, 2020

#1
+2

I will assume this is  6 (i^87)

rememeber this:             i^2 = -1         i^3 = -i           i^4 = 1

6 (i^87)    =  6  (i^4)21 * i^3     = 6* 1* -i  =   -6i

3 sqrt 2  - 6i

modulus = sqrt of both parts squared and added

sqrt(  (3 sqrt2)^2  +  (-6i)^2)

sqrt( 18 + -36(-1) ) =  sqrt 54

ElectricPavlov May 12, 2020
edited by ElectricPavlov  May 13, 2020