复数的计算题,若复数Z满足(1+2i)z=4+3i,求Z3Q

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复数的计算题,若复数Z满足(1+2i)z=4+3i,求Z3Q复数的计算题,若复数Z满足(1+2i)z=4+3i,求Z3Q复数的计算题,若复数Z满足(1+2i)z=4+3i,求Z3QZ=(4+3i)/(

复数的计算题,若复数Z满足(1+2i)z=4+3i,求Z3Q
复数的计算题,
若复数Z满足(1+2i)z=4+3i,求Z
3Q

复数的计算题,若复数Z满足(1+2i)z=4+3i,求Z3Q
Z=(4+3i)/(1+2i)
=(4+3i)(1-2i)/(1+2i)(1-2i)
=(4-8i+3i+6)/(1+4)
=(10-5i)/5
=2-i

待定系数发法
设z=a+bi
(1+2i)(a+bi)=4+3i
(a-2b)+(2a+b)i=4+3i
a-2b=4
2a+b=3
解得
a=2
b=-1
z=2-i

z=(4+3i)/(1+2i)=(4+3i)(1-2i)/5=2+i

z=(4+3i)/(1+2i)
z=(4+3i)(1-2i)/(1+2i)(1-2i)
z=(10-5i)/(1+4)
z=2-i

Z=4+3i/(1+2i)
=((4+3i)(1-2i))/((1+2i)(1-2i))
=(10-5i)\5
=2-i