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Popular >

v*v=i-5j

Solution

v \cdot v = i - 5 j

Solution

v = \frac{- 5 j + 25 j ^{2} + 1}{2} + \frac{1}{2 25 j ^{2} + 1 - 5 j} i, v = - \frac{- 5 j + 25 j ^{2} + 1}{2} - \frac{1}{2 25 j ^{2} + 1 - 5 j} i, v = - \frac{5 j + 25 j ^{2} + 1}{2} + \frac{1}{2 - \frac{5 j + 25 j ^{2} + 1}{2}} i, v = - - \frac{5 j + 25 j ^{2} + 1}{2} - \frac{1}{2 - \frac{5 j + 25 j ^{2} + 1}{2}} i

Solution steps

vv = i - 5 j

Substitute

v = x + y i

(x + y i) (x + y i) = i - 5 j

Simplify

(x + y i) (x + y i) : (x^{2} - y^{2}) + 2 i x y

(x^{2} - y^{2}) + 2 i x y = i - 5 j

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[x^{2} - y^{2} = - 5 j 2 x y = 1]

[x^{2} - y^{2} = - 5 j 2 x y = 1] : x = \frac{- 5 j + 25 j ^{2} + 1}{2}, x = - \frac{- 5 j + 25 j ^{2} + 1}{2}, x = - \frac{5 j + 25 j ^{2} + 1}{2}, x = - - \frac{5 j + 25 j ^{2} + 1}{2}, y = \frac{1}{2 25 j ^{2} + 1 - 5 j} y = - \frac{1}{2 25 j ^{2} + 1 - 5 j} y = \frac{1}{2 - \frac{5 j + 25 j ^{2} + 1}{2}} y = - \frac{1}{2 - \frac{5 j + 25 j ^{2} + 1}{2}}

Substitute back

v = x + y i

v = \frac{- 5 j + 25 j ^{2} + 1}{2} + \frac{1}{2 25 j ^{2} + 1 - 5 j} i, v = - \frac{- 5 j + 25 j ^{2} + 1}{2} - \frac{1}{2 25 j ^{2} + 1 - 5 j} i, v = - \frac{5 j + 25 j ^{2} + 1}{2} + \frac{1}{2 - \frac{5 j + 25 j ^{2} + 1}{2}} i, v = - - \frac{5 j + 25 j ^{2} + 1}{2} - \frac{1}{2 - \frac{5 j + 25 j ^{2} + 1}{2}} i

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(2+ai)/(7+bi)=3+6i

\frac{2 + ai}{7 + bi} = 3 + 6 i

4x+i(5x-y)=2+i(-3)

4 x + i (5 x - y) = 2 + i (- 3)

Frequently Asked Questions (FAQ)

What is the answer to v*v=i-5j ?
The answer to v*v=i-5j is