What is the answer to iz+(1+2i)w=25 ?

The answer to iz+(1+2i)w=25 is z=-2w+(-25+w)i

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iz+(1+2i)w=25

i z + (1 + 2 i) w = 25

z = - 2 w + (- 25 + w) i

Solution steps

i z + (1 + 2 i) w = 25

Substitute

z = x + y i

i (x + y i) + (1 + 2 i) w = 25

Expand

i (x + y i) + (1 + 2 i) w : (- y + w) + i (x + 2 w)

(- y + w) + i (x + 2 w) = 25

Rewrite

25

in standard complex form:

25 + 0 i

(- y + w) + i (x + 2 w) = 25 + 0 i

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

[- y + w = 25 x + 2 w = 0]

[- y + w = 25 x + 2 w = 0] : x = - 2 w, y = - 25 + w

Substitute back

z = x + y i

z = - 2 w + (- 25 + w) i

x^{2} + 6 + (2 x) i = 15 + 6 i

i = \frac{70 \cdot 10 e ^{- 9}}{5 s}

e = \frac{( i \cdot n ^{2} )}{( 179 )}

(x + y i)^{2} = 4 i

x + - 64 = 3 + y i

What is the answer to iz+(1+2i)w=25 ?
The answer to iz+(1+2i)w=25 is z=-2w+(-25+w)i