What is the answer to (a+2i)/(b-3i)=1+i ?

The answer to (a+2i)/(b-3i)=1+i is a=8,b=5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(a+2i)/(b-3i)=1+i

\frac{a + 2 i}{b - 3 i} = 1 + i

a = 8, b = 5

Solution steps

\frac{a + 2 i}{b - 3 i} = 1 + i

Multiply both sides by

b - 3 i

\frac{a + 2 i}{b - 3 i} (b - 3 i) = 1 \cdot (b - 3 i) + i (b - 3 i)

Simplify

a + 2 i = (b + 3) + i (- 3 + b)

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

[a = b + 3 2 = - 3 + b]

[a = b + 3 2 = - 3 + b] : a = 8, b = 5

a = 8, b = 5

(a + bi)^{2} = - 3 - 4 i

z^{2} - z = 5 - 5 i

(1 + 3 i) z^{2} + (5 + 6 i) z + 7 - 6 i = 0

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

∣ z ∣^{2} + z - 3 i = 11

What is the answer to (a+2i)/(b-3i)=1+i ?
The answer to (a+2i)/(b-3i)=1+i is a=8,b=5