Write -4i + (1/4-5i)-(-3/4+8i)+17i as a complex number in standard form

Mathematics

1 answer:

Alex17521 [72]2 years ago

5 0

Answer:

Step-by-step explanation:

$-4i+\left(\dfrac{1}{4}-5i\right)-\left(-\dfrac{3}{4}+8i\right)+17i\\\\=-4i+\dfrac{1}{4}-5i+\dfrac{3}{4}-8i+17i\\\\=\left(\dfrac{1}{4}+\dfrac{3}{4}\right)+(-4i-5i-8i+17i)\\\\=\dfrac{1+3}{4}+(-4-5-8+17)i\\\\=\dfrac{4}{4}+0i\\\\=1$

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The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points $(-4,\ -1)$ and $\left(\dfrac{1}{2},\ 3\right)$ .

Substitute:

$m=\dfrac{3-(-1)}{\frac{1}{2}-(-4)}=\dfrac{4}{4\frac{1}{2}}=\dfrac{4}{\frac{9}{2}}=4\cdot\dfrac{2}{9}=\dfrac{8}{9}\\\\y-(-1)=\dfrac{8}{9}(x-(-4))\\\\y+1=\dfrac{8}{9}(x+4)$

The standard form: Ax + By = C

$y+1=\dfrac{8}{9}(x+4)\qquad\text{multiply both sides by 9}\\\\9y+9=8(x+4)\qquad\text{use distributive property}\\\\9y+9=8x+32\qquad\text{subtract 9 from both sides}\\\\9y=8x+23\qquad\text{subtract 8x from both sides}\\\\-8x+9y=23\qquad\text{change the signs}\\\\\boxed{8x-9y=23}$