Complex Number to Rectangular Form?

Question

Write each complex number in rectangular form.

NOTE: the letter d = degrees. Got it?

(1) 3(cos210d + isin210d)

(2) 4(cos(pi/2) + isin(pi/2))

Answer 1

(1) 3(cos210d + isin210d)
3(-sqrt(3)/2 + i 1/2)

(2) 4(cos(pi/2) + isin(pi/2))
4(0+1i)

Answer 2

(1) 3(Cos 7pi/6 + iSin(7pi/6))
(2) 4(Cos 90' + iSin 90)

pi = 180'

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amal
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Answer 3

it rather is often written as rcosa + jsina = 5/sqrt 2+ 5/sqrtj (z= rcosa + jsina} equating real and imag rcosa= 5/sqrt(2) rsina = 5/sqrt(2) squaring and including r^2( cos^2a+sin^2a) = 25/2+25/2= 50/2 =25 r^2(a million)=25 (cos^2a+sin^2a=a million) r= 5 (taking purely the beneficial value) rcosa = 5/sqrt2 cosa= 5/rsqrt 2= 5/5sqrt(2) = a million/sqrt2 sina= a million/sqrt(2) sin cos the two are positve so perspective a lies in first quadrant and for 40 5 stages it rather is for pie/4 sin cos the two are a million/sqrt(2) so now the complicated extensive variety is r[cosa +jsina]= 5[cospi/4+jsinpi/4]= 5[e^jpi/4] as cosa + isina = e^ia now( z1)^3 =[ 5[e^jpi/4]]^3 = 5^3[ e^3jpi/4] = 125e^3jpi/4 consequently the soln