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The reciprocal of a + bi is a - bi:

1/(a + bi) since the conjugate is a - bi:

= 1(a - bi)/[(a + bi)(a - bi)]

= (a - bi)/[a2 - (b2)(i2)] since i2 equals to -1:

= (a - bi)/(a2 + b2) since a2 + b2 = 1:

= a - bi/1

= a - bi

Q: What is the reciprocal of a plus bi if a2 plus b2 equals 1?

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a2

Pythagorean Theorem

a right triangle

All you need to do is substitute the given values of a and c into the equation, then solve for c: a2 + c2 = b2 102 + 302 = b2 100 + 900 = b2 b2 = 1000 b = √1000 b = 10√10

a2 + b2 + c2 - ab - bc - ca = 0 => 2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca = 0 Rearranging, a2 - 2ab + b2 + b2 - 2bc + c2 + c2 - 2ca + a2 = 0 => (a2 - 2ab + b2) + (b2 - 2bc + c2) + (c2 - 2ca + a2) = 0 or (a - b)2 + (b - c)2 + (c - a)2 = 0 so a - b = 0, b - c = 0 and c - a = 0 (since each square is >=0) that is, a = b = c

Related questions

a2

l a2 b2 is c2!!Its completely norma

Pythagorean Theorem

a right triangle

A2 + B2 = C2 If C=8, then A2 + B2 = 64

a2+b2+c2=x2+y2+z2 divide each side by 2 (a2+b2+c2)/2=(x2+y2+z2)/2 a+b+c=x+y+z

You just typed it.

a2+2a2b+2ab2+b2

Pythagoras' theorem for a right angle triangle.

All you need to do is substitute the given values of a and c into the equation, then solve for c: a2 + c2 = b2 102 + 302 = b2 100 + 900 = b2 b2 = 1000 b = √1000 b = 10√10

a2 + b2 + c2 - ab - bc - ca = 0 => 2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca = 0 Rearranging, a2 - 2ab + b2 + b2 - 2bc + c2 + c2 - 2ca + a2 = 0 => (a2 - 2ab + b2) + (b2 - 2bc + c2) + (c2 - 2ca + a2) = 0 or (a - b)2 + (b - c)2 + (c - a)2 = 0 so a - b = 0, b - c = 0 and c - a = 0 (since each square is >=0) that is, a = b = c

This is known as the Cosine Rule.