Identify the real and imaginary parts of each complex number. 3 + 2 i 3 3+2i\sqrt3 3 + 2 i 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

So here, I wanna identify the real and imaginary parts of this complex number, and I have 3+2i root 3. Now remember the real part of my number is just that number that's out there by itself, my real number. So a, in this case, is 3. That's my real part. Now the imaginary part is absolutely everything that is multiplying that I. So in this case, I have a 2 in the front, but I also have the square root of 3. So that means that b, the imaginary part, is actually 2 root 3 because those are both multiplying by imaginary number I.

Identify the real and imaginary parts of each complex number. 3 + 2 i 3 3+2i\sqrt3 3 + 2 i 3 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

a = 3 , b = 2 3 a=3,b=2\sqrt3 a = 3 , b = 2 3 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

a = 3 , b = 2 a = 3, b = 2 a = 3 , b = 2

a = 2 3 , b = 3 a=2\sqrt3,b=3 a = 2 3 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z"> , b = 3

a = 3 , b = 3 a=3,b=\sqrt3 a = 3 , b = 3 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

0. Review of College Algebra

Complex Numbers

Trigonometry

0. Review of College Algebra

Complex Numbers

Struggling with Trigonometry?

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Multiple Choice

Identify the real and imaginary parts of each complex number.
$3+2i\sqrt3$

$a=3,b=2\sqrt3$

$a = 3, b = 2$

$a=2\sqrt3,b=3$

$a=3,b=\sqrt3$

Verified step by step guidance

Identify the standard form of a complex number, which is a + bi, where 'a' is the real part and 'b' is the imaginary part.

Examine the given complex number: 3 + 2i√3.

Determine the real part 'a' of the complex number, which is the coefficient of the real number without the imaginary unit 'i'. In this case, 'a' is 3.

Determine the imaginary part 'b' of the complex number, which is the coefficient of the imaginary unit 'i'. In this case, 'b' is 2√3.

Conclude that the real part is 3 and the imaginary part is 2√3, matching the format a = 3, b = 2√3.

3:31m

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Struggling with Trigonometry?

Identify the real and imaginary parts of each complex number. 3+2i33+2i\sqrt33+2i3

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Complex Numbers practice set

Identify the real and imaginary parts of each complex number.
$3+2i\sqrt3$