What is the answer to 7r=3t^2i-2j ?

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7r=3t^2i-2j

7 r = 3 t^{2} i - 2 j

(r = - \frac{2 j}{7}, t = 0)

Solution steps

7 r = 3 t^{2} i - 2 j

Rewrite

7 r

in standard complex form:

7 r + 0 i

7 r + 0 i = 3 t^{2} i - 2 j

Rewrite

3 t^{2} i - 2 j

in standard complex form:

- 2 j + 3 t^{2} i

7 r + 0 i = - 2 j + 3 t^{2} i

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

[7 r = - 2 j 0 = 3 t^{2}]

[7 r = - 2 j 0 = 3 t^{2}] : (r = - \frac{2 j}{7}, t = 0)

(r = - \frac{2 j}{7}, t = 0)

i z^{2} - (2 + 3 i) z + 1 + 5 i = 0

(x + y i)^{2} = 5 + 12 i

z^{2} (3 - i) + 5 (1 - i) (1 + i) + 2 + 16 i = 0

y, s i x^{2} + y^{2} = z^{2}

\frac{( 2 - 3 i )}{2 x + y i} = 3 + 2 i