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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

a(1+2i)+b(2-3i)=5+3i

a (1 + 2 i) + b (2 - 3 i) = 5 + 3 i

a = 3, b = 1

Solution steps

a (1 + 2 i) + b (2 - 3 i) = 5 + 3 i

Rewrite

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

in standard complex form:

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

(a + 2 b) + (2 a - 3 b) i = 5 + 3 i

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

[a + 2 b = 5 2 a - 3 b = 3]

[a + 2 b = 5 2 a - 3 b = 3] : a = 3, b = 1

a = 3, b = 1

- 4 i + 4 y - 8 = - 2 + x i + 5 x

z^{2} + (5 + 6 i) z - 3 + 15 i = 0

- 3 i + 4 y = - 2 + x i

y, (2 x - y) - 16 i = 10 + 4

x + 5 y + i 2 = 8 + (2 x - 4 y) i

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