Question

z1=2+3i z2=2-3i z1+z2= z1-z2= z1:z1=​

Answer 1

z1=2+3i

z2=2-3i

• z1+z2= 2+3i + 2-3i = 4

• z1-z2= 2+3i - (2-3i) = 2+3i-2+3i = 6i

• z1:z1=

$= {}^{2 + 3i)}\frac{2 + 3i}{2 - 3i} = \frac{(2 + 3i) {}^{2} }{(2 + 3i)(2 - 3i)} = \\ \\ = \frac{2 {}^{2} + 2 \times 2 \times 3i + (3i) {}^{2} }{2 {}^{2} - (3i) {}^{2} } = \\ \\ = \frac{4 + 12i - 9}{4 - ( - 9)} = \frac{5 - 12i}{4 + 9} = \\ \\ = \frac{5 - 12i}{13} = \frac{5}{13} - \frac{12}{13} i$

IMPORTANT:

$\boxed{\orange{ {i}^{2} = - 1}}$

(a+b)² = a² + 2ab + b²

(a+b)(a-b) = a²- b²