Question

Write the expression in standard form.

Answer 1

\[\frac{ 7 }{ 3-15i }\]

Answer 2

@jim_thompson5910

Answer 3

Standard form?

Answer 4

I think it's a+bi if a=0 and b can't =0

Answer 5

Oh ok, sec

Answer 6

multiply top and bottom by 3+15i

Answer 7

the reason why this is done is because (a+bi)(a-bi) = a^2 + b^2 which effectively converts the denominator into a real number

Answer 8

okay, I got (21+105i)/(9-225i^2) is this right so far?

Answer 9

Wait... I think I might have it... Is (7+35i)/78 correct?

Answer 10

225i^2 = 225(-1) = -225

so 9-225i^2 = 9 - (-225) = 9 + 225 = 234

Answer 11

(7+35i)/78 is correct after fully simplifying/reducing

Answer 12

Do you think you could help me with one more?

Answer 13

sure, go for it

Answer 14

Find the real numbers x and y that make the equation true.
-3 + yi = x + 6i

Answer 15

@jim_thompson5910

Answer 16

The real part of -3+yi is -3

The real part of x+6i is x

so x = -3 since the real parts are equal

Answer 17

the imaginary part of -3+yi is yi
the imaginary part of x+6i is 6i

So


yi = 6i

y = 6